{"version":"1.0.0","segments":[{"speaker":"Greg","startTime":5.25,"endTime":8.13,"body":"Hi everybody, my name is"},{"speaker":"Greg","startTime":5.25,"endTime":8.13,"body":"Greg Hancock and along with my"},{"speaker":"Greg","startTime":8.13,"endTime":10.98,"body":"asymptotically efficient friend"},{"speaker":"Greg","startTime":8.13,"endTime":10.98,"body":"Patrick Curran, we make a"},{"speaker":"Greg","startTime":10.98,"endTime":13.62,"body":"quantity food. We're a podcast"},{"speaker":"Greg","startTime":10.98,"endTime":13.62,"body":"dedicated to all things"},{"speaker":"Greg","startTime":13.62,"endTime":16.38,"body":"quantitative, ranging from the"},{"speaker":"Greg","startTime":13.62,"endTime":16.38,"body":"irrelevant to the completely"},{"speaker":"Greg","startTime":16.38,"endTime":19.53,"body":"irrelevant. In this episode we"},{"speaker":"Greg","startTime":16.38,"endTime":19.53,"body":"talk about maximum likelihood"},{"speaker":"Greg","startTime":19.53,"endTime":23.25,"body":"estimation, what it is, where it"},{"speaker":"Greg","startTime":19.53,"endTime":23.25,"body":"comes from, how it works, what"},{"speaker":"Greg","startTime":23.25,"endTime":27.42,"body":"it can do and what it can't do."},{"speaker":"Greg","startTime":23.25,"endTime":27.42,"body":"Along the way, we also mentioned"},{"speaker":"Greg","startTime":27.84,"endTime":32.55,"body":"tour bombing your kid licking"},{"speaker":"Greg","startTime":27.84,"endTime":32.55,"body":"the turtle, Van Halen and ACDC"},{"speaker":"Greg","startTime":32.94,"endTime":38.31,"body":"orange mustaches, brandy snifter"},{"speaker":"Greg","startTime":32.94,"endTime":38.31,"body":"Pong, bus number 27. Rodney"},{"speaker":"Greg","startTime":38.31,"endTime":43.17,"body":"Fisher, why people hate us,"},{"speaker":"Greg","startTime":38.31,"endTime":43.17,"body":"circus tents, night parachuting,"},{"speaker":"Greg","startTime":43.56,"endTime":47.88,"body":"flat spots, lazy parabolas,"},{"speaker":"Greg","startTime":43.56,"endTime":47.88,"body":"vanilla ice cream, and"},{"speaker":"Greg","startTime":47.88,"endTime":51.09,"body":"statistical bouncers. We hope"},{"speaker":"Greg","startTime":47.88,"endTime":51.09,"body":"you enjoyed today's episode."},{"speaker":"Patrick","startTime":52.11,"endTime":55.26,"body":"So I couldn't help but"},{"speaker":"Patrick","startTime":52.11,"endTime":55.26,"body":"notice that you just took your"},{"speaker":"Patrick","startTime":55.26,"endTime":57.96,"body":"own sweet ass time to join us"},{"speaker":"Patrick","startTime":55.26,"endTime":57.96,"body":"here today."},{"speaker":"Greg","startTime":58.32,"endTime":62.7,"body":"I am sorry, I am sorry, I"},{"speaker":"Greg","startTime":58.32,"endTime":62.7,"body":"hate being late. So one of the"},{"speaker":"Greg","startTime":62.7,"endTime":66.63,"body":"things about me early is on time"},{"speaker":"Greg","startTime":62.7,"endTime":66.63,"body":"on time is late and I was"},{"speaker":"Greg","startTime":66.63,"endTime":69.24,"body":"actually late late and I really,"},{"speaker":"Greg","startTime":66.63,"endTime":69.24,"body":"really apologize."},{"speaker":"Patrick","startTime":69.27,"endTime":72.78,"body":"So let's hear your air"},{"speaker":"Patrick","startTime":69.27,"endTime":72.78,"body":"quote. Excuse. Honestly, it's"},{"speaker":"Patrick","startTime":72.78,"endTime":73.08,"body":"not that"},{"speaker":"Greg","startTime":73.38,"endTime":77.67,"body":"my son Quinn is taking a"},{"speaker":"Greg","startTime":73.38,"endTime":77.67,"body":"tour of campus with his really"},{"speaker":"Greg","startTime":77.67,"endTime":80.43,"body":"good friend Alex. They're"},{"speaker":"Greg","startTime":77.67,"endTime":80.43,"body":"walking around doing the"},{"speaker":"Greg","startTime":80.46,"endTime":84.48,"body":"official University of Maryland"},{"speaker":"Greg","startTime":80.46,"endTime":84.48,"body":"tour. And I went and tour bombed"},{"speaker":"Greg","startTime":84.48,"endTime":93.3,"body":"them. So I snuck up really bad."},{"speaker":"Greg","startTime":84.48,"endTime":93.3,"body":"Oh, geez. Well, anyway, it did"},{"speaker":"Greg","startTime":93.3,"endTime":97.17,"body":"my heart good to sneak up in"},{"speaker":"Greg","startTime":93.3,"endTime":97.17,"body":"there and be a part of the tour"},{"speaker":"Greg","startTime":97.17,"endTime":100.23,"body":"and, and to see my kid you know,"},{"speaker":"Greg","startTime":97.17,"endTime":100.23,"body":"as he's making important"},{"speaker":"Greg","startTime":100.23,"endTime":103.02,"body":"decisions. It was so cool"},{"speaker":"Greg","startTime":100.23,"endTime":103.02,"body":"though. Just listening to the"},{"speaker":"Greg","startTime":103.02,"endTime":106.86,"body":"tour guide, you know, really"},{"speaker":"Greg","startTime":103.02,"endTime":106.86,"body":"inspirational college aged kid"},{"speaker":"Greg","startTime":107.1,"endTime":110.43,"body":"talking about all the great"},{"speaker":"Greg","startTime":107.1,"endTime":110.43,"body":"things that those students can"},{"speaker":"Greg","startTime":110.43,"endTime":112.8,"body":"achieve. While here at Maryland."},{"speaker":"Greg","startTime":110.43,"endTime":112.8,"body":"It was nice. I got a little"},{"speaker":"Greg","startTime":112.8,"endTime":113.34,"body":"teary."},{"speaker":"Patrick","startTime":113.399,"endTime":116.549,"body":"I bet you did."},{"speaker":"Patrick","startTime":113.399,"endTime":116.549,"body":"Especially when everybody was"},{"speaker":"Patrick","startTime":116.549,"endTime":121.259,"body":"made to lick the E. coli turtle"},{"speaker":"Patrick","startTime":116.549,"endTime":121.259,"body":"on the quad. Isn't that the"},{"speaker":"Patrick","startTime":121.259,"endTime":122.039,"body":"tradition?"},{"speaker":"Greg","startTime":122.55,"endTime":125.34,"body":"You don't have to lick it,"},{"speaker":"Greg","startTime":122.55,"endTime":125.34,"body":"you can just rub it with your"},{"speaker":"Greg","startTime":125.34,"endTime":127.53,"body":"hand lifting is completely"},{"speaker":"Greg","startTime":125.34,"endTime":127.53,"body":"optional."},{"speaker":"Patrick","startTime":128.88,"endTime":133.77,"body":"And you know, we've"},{"speaker":"Patrick","startTime":128.88,"endTime":133.77,"body":"done our tour kind of things."},{"speaker":"Patrick","startTime":133.77,"endTime":137.13,"body":"And I love that you can be"},{"speaker":"Patrick","startTime":133.77,"endTime":137.13,"body":"anything you can do anything"},{"speaker":"Patrick","startTime":137.19,"endTime":144.75,"body":"right? And all made me think of"},{"speaker":"Patrick","startTime":137.19,"endTime":144.75,"body":"is almost TV game show. And what"},{"speaker":"Patrick","startTime":144.75,"endTime":150.6,"body":"did you accomplish by age 20?"},{"speaker":"Patrick","startTime":144.75,"endTime":150.6,"body":"Because I think we are part of"},{"speaker":"Patrick","startTime":150.6,"endTime":155.43,"body":"an entire generation that came"},{"speaker":"Patrick","startTime":150.6,"endTime":155.43,"body":"up through the most boring part"},{"speaker":"Patrick","startTime":155.43,"endTime":161.01,"body":"of history in terms of having"},{"speaker":"Patrick","startTime":155.43,"endTime":161.01,"body":"your character melded in the"},{"speaker":"Patrick","startTime":161.01,"endTime":165.12,"body":"furnace of Oh my god. Yes."},{"speaker":"Patrick","startTime":161.01,"endTime":165.12,"body":"stress and strain. It's like"},{"speaker":"Patrick","startTime":165.12,"endTime":170.64,"body":"yeah, no. By age 21 of my"},{"speaker":"Patrick","startTime":165.12,"endTime":170.64,"body":"greatest achievements has been I"},{"speaker":"Patrick","startTime":170.64,"endTime":173.61,"body":"saw Van Halen both with David"},{"speaker":"Patrick","startTime":170.64,"endTime":173.61,"body":"Lee Roth"},{"speaker":"Patrick","startTime":180.06,"endTime":181.65,"body":"and Sammy Hagar."},{"speaker":"Patrick","startTime":190.2,"endTime":196.32,"body":"No much this in perspective, my"},{"speaker":"Patrick","startTime":190.2,"endTime":196.32,"body":"great grandfather came over on a"},{"speaker":"Patrick","startTime":196.32,"endTime":204.69,"body":"famine ship from Ireland at age"},{"speaker":"Patrick","startTime":196.32,"endTime":204.69,"body":"16, unaccompanied. His son then"},{"speaker":"Patrick","startTime":204.72,"endTime":210.45,"body":"founded a printing company, his"},{"speaker":"Patrick","startTime":204.72,"endTime":210.45,"body":"son, who was my father was born"},{"speaker":"Patrick","startTime":210.45,"endTime":216.87,"body":"nine months after the stock"},{"speaker":"Patrick","startTime":210.45,"endTime":216.87,"body":"market crash in 1929. And did"},{"speaker":"Patrick","startTime":216.9,"endTime":223.56,"body":"soup can collections for steel"},{"speaker":"Patrick","startTime":216.9,"endTime":223.56,"body":"for World War Two. And I saw"},{"speaker":"Patrick","startTime":223.56,"endTime":227.19,"body":"both David Lee Roth and Sammy"},{"speaker":"Patrick","startTime":223.56,"endTime":227.19,"body":"Hagar"},{"speaker":"Greg","startTime":227.61,"endTime":230.01,"body":"later we're going to"},{"speaker":"Greg","startTime":227.61,"endTime":230.01,"body":"expect great things from that"},{"speaker":"Greg","startTime":230.01,"endTime":230.67,"body":"Patrick."},{"speaker":"Patrick","startTime":232.38,"endTime":236.13,"body":"Nice still pales in"},{"speaker":"Patrick","startTime":232.38,"endTime":236.13,"body":"comparison is, you know, famine"},{"speaker":"Patrick","startTime":236.13,"endTime":239.34,"body":"ship. Your grandmother survived"},{"speaker":"Patrick","startTime":236.13,"endTime":239.34,"body":"Auschwitz."},{"speaker":"Greg","startTime":239.4,"endTime":243.81,"body":"Yes, she did. And it kind"},{"speaker":"Greg","startTime":239.4,"endTime":243.81,"body":"of makes anything that I do. You"},{"speaker":"Greg","startTime":243.81,"endTime":248.52,"body":"know, I can only disappoint. By"},{"speaker":"Greg","startTime":243.81,"endTime":248.52,"body":"the time I was age 20 or 21. I"},{"speaker":"Greg","startTime":248.52,"endTime":250.98,"body":"had gotten kicked out of a"},{"speaker":"Greg","startTime":248.52,"endTime":250.98,"body":"college honors program and I"},{"speaker":"Greg","startTime":250.98,"endTime":252.45,"body":"grew an orange moustache."},{"speaker":"Patrick","startTime":254.61,"endTime":257.61,"body":"It does make me start"},{"speaker":"Patrick","startTime":254.61,"endTime":257.61,"body":"thinking about when do you make"},{"speaker":"Patrick","startTime":257.61,"endTime":260.22,"body":"your great achievements and"},{"speaker":"Patrick","startTime":257.61,"endTime":260.22,"body":"again, with things like"},{"speaker":"Patrick","startTime":260.37,"endTime":264.39,"body":"mathematics as people talk about"},{"speaker":"Patrick","startTime":260.37,"endTime":264.39,"body":"that, if you haven't made a"},{"speaker":"Patrick","startTime":264.39,"endTime":269.49,"body":"truly great achievement by your"},{"speaker":"Patrick","startTime":264.39,"endTime":269.49,"body":"mid 20s. You're not going to"},{"speaker":"Patrick","startTime":269.55,"endTime":274.44,"body":"Yeah, which makes me very sad."},{"speaker":"Patrick","startTime":269.55,"endTime":274.44,"body":"One of my favorite early"},{"speaker":"Patrick","startTime":274.44,"endTime":278.73,"body":"achievers is our A Fisher and"},{"speaker":"Patrick","startTime":274.44,"endTime":278.73,"body":"we've talked about on prior"},{"speaker":"Patrick","startTime":278.73,"endTime":283.8,"body":"episodes, we also want to"},{"speaker":"Patrick","startTime":278.73,"endTime":283.8,"body":"embrace what our history is. In"},{"speaker":"Patrick","startTime":283.8,"endTime":288.33,"body":"one part, Fisher was a very"},{"speaker":"Patrick","startTime":283.8,"endTime":288.33,"body":"unpleasant human being and for a"},{"speaker":"Patrick","startTime":288.33,"endTime":291.66,"body":"period of time had very"},{"speaker":"Patrick","startTime":288.33,"endTime":291.66,"body":"unpleasant philosophical beliefs"},{"speaker":"Patrick","startTime":291.66,"endTime":296.61,"body":"and dedications. On the other"},{"speaker":"Patrick","startTime":291.66,"endTime":296.61,"body":"hand, developed analysis of"},{"speaker":"Patrick","startTime":296.61,"endTime":302.94,"body":"variance analysis of covariance"},{"speaker":"Patrick","startTime":296.61,"endTime":302.94,"body":"degrees. sort of freedom. And in"},{"speaker":"Patrick","startTime":302.94,"endTime":306.99,"body":"his 20s, what we might kick"},{"speaker":"Patrick","startTime":302.94,"endTime":306.99,"body":"around a little bit here today,"},{"speaker":"Patrick","startTime":307.23,"endTime":312.21,"body":"maximum likelihood estimation."},{"speaker":"Patrick","startTime":307.23,"endTime":312.21,"body":"And what did you do by age 20?"},{"speaker":"Patrick","startTime":312.21,"endTime":313.2,"body":"Dr. Hancock?"},{"speaker":"Greg","startTime":313.92,"endTime":315.54,"body":"Did I mention the orange"},{"speaker":"Greg","startTime":313.92,"endTime":315.54,"body":"mustache?"},{"speaker":"Patrick","startTime":317.369,"endTime":319.589,"body":"We'll do the orange"},{"speaker":"Patrick","startTime":317.369,"endTime":319.589,"body":"come from"},{"speaker":"Greg","startTime":319.68,"endTime":322.92,"body":"I was born with red hair."},{"speaker":"Greg","startTime":319.68,"endTime":322.92,"body":"And so I always sort of had this"},{"speaker":"Greg","startTime":322.92,"endTime":326.55,"body":"underlying red that was dormant."},{"speaker":"Greg","startTime":322.92,"endTime":326.55,"body":"And then by the time I was able"},{"speaker":"Greg","startTime":326.55,"endTime":329.4,"body":"to grow mustache and beard, it"},{"speaker":"Greg","startTime":326.55,"endTime":329.4,"body":"came out looking like I had"},{"speaker":"Greg","startTime":329.4,"endTime":333.57,"body":"creamsicle on my Tell me one"},{"speaker":"Patrick","startTime":333.57,"endTime":336.0,"body":"thing that"},{"speaker":"Patrick","startTime":333.57,"endTime":336.0,"body":"characterized you in your early"},{"speaker":"Patrick","startTime":336.0,"endTime":339.9,"body":"20s, set against the stage of"},{"speaker":"Patrick","startTime":336.0,"endTime":339.9,"body":"degrees of freedom and maximum"},{"speaker":"Patrick","startTime":339.9,"endTime":340.47,"body":"likelihood."},{"speaker":"Greg","startTime":340.77,"endTime":343.11,"body":"Do you mean one"},{"speaker":"Greg","startTime":340.77,"endTime":343.11,"body":"achievement? Yeah. All right. I"},{"speaker":"Greg","startTime":343.11,"endTime":346.11,"body":"have no idea what my actual"},{"speaker":"Greg","startTime":343.11,"endTime":346.11,"body":"achievements were. I think there"},{"speaker":"Greg","startTime":346.11,"endTime":349.74,"body":"weren't a whole lot of them. But"},{"speaker":"Greg","startTime":346.11,"endTime":349.74,"body":"along the lines of you, I saw"},{"speaker":"Greg","startTime":349.77,"endTime":352.62,"body":"ACDC six times. Oh,"},{"speaker":"Patrick","startTime":353.7,"endTime":358.05,"body":"okay. I am truly"},{"speaker":"Patrick","startTime":353.7,"endTime":358.05,"body":"impressed. Okay, because you"},{"speaker":"Patrick","startTime":358.05,"endTime":360.48,"body":"know what, I have never seen a"},{"speaker":"Patrick","startTime":358.05,"endTime":360.48,"body":"CDC."},{"speaker":"Greg","startTime":362.07,"endTime":365.52,"body":"It's a shame. Angus is"},{"speaker":"Greg","startTime":362.07,"endTime":365.52,"body":"crazy amazing. Even at the age"},{"speaker":"Greg","startTime":365.52,"endTime":366.21,"body":"he is now."},{"speaker":"Patrick","startTime":368.19,"endTime":371.67,"body":"So why are we talking"},{"speaker":"Patrick","startTime":368.19,"endTime":371.67,"body":"about maximum likelihood? First"},{"speaker":"Patrick","startTime":371.7,"endTime":377.58,"body":"is it's cool as crapola. Second,"},{"speaker":"Patrick","startTime":371.7,"endTime":377.58,"body":"last week, we kicked around"},{"speaker":"Patrick","startTime":377.58,"endTime":380.76,"body":"ordinary least squares. Yeah."},{"speaker":"Patrick","startTime":377.58,"endTime":380.76,"body":"And we talked about if your"},{"speaker":"Patrick","startTime":380.76,"endTime":386.7,"body":"camel wanders off, does it drop"},{"speaker":"Patrick","startTime":380.76,"endTime":386.7,"body":"off the edge of a disk? Does it"},{"speaker":"Patrick","startTime":386.73,"endTime":392.67,"body":"walk on a plane? That's a that's"},{"speaker":"Patrick","startTime":386.73,"endTime":392.67,"body":"a Kindle, it just never comes"},{"speaker":"Patrick","startTime":392.67,"endTime":397.11,"body":"back. Okay? Or is it a sphere"},{"speaker":"Patrick","startTime":392.67,"endTime":397.11,"body":"where your camera comes back,"},{"speaker":"Patrick","startTime":397.11,"endTime":401.7,"body":"but scares the crap out of you?"},{"speaker":"Patrick","startTime":397.11,"endTime":401.7,"body":"Because now he's behind you. And"},{"speaker":"Patrick","startTime":401.7,"endTime":405.45,"body":"so we talked about Genesis of"},{"speaker":"Patrick","startTime":401.7,"endTime":405.45,"body":"least squares characteristics,"},{"speaker":"Patrick","startTime":405.48,"endTime":408.81,"body":"and how there are some really"},{"speaker":"Patrick","startTime":405.48,"endTime":408.81,"body":"magical properties of least"},{"speaker":"Patrick","startTime":408.81,"endTime":414.0,"body":"squares. But Fisher, who was not"},{"speaker":"Patrick","startTime":408.81,"endTime":414.0,"body":"tempted to see Van Halen, or AC"},{"speaker":"Patrick","startTime":414.0,"endTime":418.8,"body":"DC, he was able to identify"},{"speaker":"Patrick","startTime":414.0,"endTime":418.8,"body":"certain limitations of those"},{"speaker":"Patrick","startTime":418.8,"endTime":422.31,"body":"approaches. Yeah. And invented"},{"speaker":"Patrick","startTime":418.8,"endTime":422.31,"body":"maximum like, that's right."},{"speaker":"Greg","startTime":422.34,"endTime":425.43,"body":"So he stopped playing beer"},{"speaker":"Greg","startTime":422.34,"endTime":425.43,"body":"pong, as he was wanting to do"},{"speaker":"Patrick","startTime":427.74,"endTime":432.63,"body":"it think it was brandy"},{"speaker":"Patrick","startTime":427.74,"endTime":432.63,"body":"snifter upon at that point. So"},{"speaker":"Patrick","startTime":432.63,"endTime":435.18,"body":"much class? Exactly, exactly."},{"speaker":"Patrick","startTime":432.63,"endTime":435.18,"body":"Yeah. So"},{"speaker":"Greg","startTime":435.18,"endTime":438.03,"body":"this was Fisher's, I don't"},{"speaker":"Greg","startTime":435.18,"endTime":438.03,"body":"want to say answer to least"},{"speaker":"Greg","startTime":438.03,"endTime":440.64,"body":"squares. But if you think about"},{"speaker":"Greg","startTime":438.03,"endTime":440.64,"body":"trying to figure out what is a"},{"speaker":"Greg","startTime":440.64,"endTime":443.25,"body":"best fitting model, we talked"},{"speaker":"Greg","startTime":440.64,"endTime":443.25,"body":"about the least squares"},{"speaker":"Greg","startTime":443.25,"endTime":446.7,"body":"criterion as one way to"},{"speaker":"Greg","startTime":443.25,"endTime":446.7,"body":"characterize that, and that has"},{"speaker":"Greg","startTime":446.7,"endTime":450.33,"body":"legs that extend into many"},{"speaker":"Greg","startTime":446.7,"endTime":450.33,"body":"dimensions, because you go past"},{"speaker":"Greg","startTime":450.33,"endTime":453.42,"body":"simple regression into the"},{"speaker":"Greg","startTime":450.33,"endTime":453.42,"body":"multivariate world, and least"},{"speaker":"Greg","startTime":453.42,"endTime":456.81,"body":"squares carries forward, it"},{"speaker":"Greg","startTime":453.42,"endTime":456.81,"body":"really does a good job. But he"},{"speaker":"Greg","startTime":456.81,"endTime":461.13,"body":"had a very, very different way"},{"speaker":"Greg","startTime":456.81,"endTime":461.13,"body":"of looking at this idea of fit"},{"speaker":"Greg","startTime":461.16,"endTime":464.64,"body":"and models. And it was"},{"speaker":"Greg","startTime":461.16,"endTime":464.64,"body":"incredibly clever. And damn it,"},{"speaker":"Greg","startTime":464.64,"endTime":466.65,"body":"if he wasn't like 22 years old."},{"speaker":"Greg","startTime":464.64,"endTime":466.65,"body":"It was"},{"speaker":"Patrick","startTime":466.65,"endTime":470.28,"body":"another instance of"},{"speaker":"Patrick","startTime":466.65,"endTime":470.28,"body":"Calvin Ball, where we talked"},{"speaker":"Patrick","startTime":470.28,"endTime":475.41,"body":"about last week of let's"},{"speaker":"Patrick","startTime":470.28,"endTime":475.41,"body":"redefine what we mean by best,"},{"speaker":"Patrick","startTime":475.44,"endTime":479.67,"body":"right, and what we're going to"},{"speaker":"Patrick","startTime":475.44,"endTime":479.67,"body":"maximize or minimize, depending"},{"speaker":"Patrick","startTime":479.67,"endTime":484.47,"body":"upon how you go about doing"},{"speaker":"Patrick","startTime":479.67,"endTime":484.47,"body":"things. And maximum likelihood"},{"speaker":"Patrick","startTime":484.5,"endTime":489.18,"body":"is approaching the very same"},{"speaker":"Patrick","startTime":484.5,"endTime":489.18,"body":"problem. That is, we believe"},{"speaker":"Patrick","startTime":489.18,"endTime":493.26,"body":"these parameters to exist in the"},{"speaker":"Patrick","startTime":489.18,"endTime":493.26,"body":"population, we are unable to"},{"speaker":"Patrick","startTime":493.26,"endTime":498.15,"body":"observe them directly. And we"},{"speaker":"Patrick","startTime":493.26,"endTime":498.15,"body":"want to obtain the best possible"},{"speaker":"Patrick","startTime":498.15,"endTime":501.93,"body":"estimates of those given our"},{"speaker":"Patrick","startTime":498.15,"endTime":501.93,"body":"sample data. And he just"},{"speaker":"Patrick","startTime":501.93,"endTime":505.41,"body":"shrugged and said, I actually"},{"speaker":"Patrick","startTime":501.93,"endTime":505.41,"body":"have another way of defining"},{"speaker":"Patrick","startTime":505.41,"endTime":509.91,"body":"best and develop this whole new"},{"speaker":"Patrick","startTime":505.41,"endTime":509.91,"body":"class of estimators, which, as"},{"speaker":"Patrick","startTime":509.91,"endTime":514.83,"body":"we'll see, really is the coin of"},{"speaker":"Patrick","startTime":509.91,"endTime":514.83,"body":"the realm in almost everything"},{"speaker":"Patrick","startTime":514.83,"endTime":515.4,"body":"that we do."},{"speaker":"Greg","startTime":515.46,"endTime":518.13,"body":"Yeah, maximum likelihood"},{"speaker":"Greg","startTime":515.46,"endTime":518.13,"body":"is something that gets really"},{"speaker":"Greg","startTime":518.13,"endTime":522.21,"body":"hairy when it starts to get big"},{"speaker":"Greg","startTime":518.13,"endTime":522.21,"body":"in terms of the models and other"},{"speaker":"Greg","startTime":522.21,"endTime":524.61,"body":"things. But I don't want to"},{"speaker":"Greg","startTime":522.21,"endTime":524.61,"body":"spoil it. And we don't need to"},{"speaker":"Greg","startTime":524.61,"endTime":527.37,"body":"start there. Let's start small."},{"speaker":"Greg","startTime":524.61,"endTime":527.37,"body":"Do you have maybe a little"},{"speaker":"Greg","startTime":527.37,"endTime":530.37,"body":"example just to plant some of"},{"speaker":"Greg","startTime":527.37,"endTime":530.37,"body":"the ideas of what maximum"},{"speaker":"Greg","startTime":530.37,"endTime":533.34,"body":"likelihood is and how it helps"},{"speaker":"Greg","startTime":530.37,"endTime":533.34,"body":"us to think about things I"},{"speaker":"Patrick","startTime":533.37,"endTime":536.97,"body":"do? It was at this"},{"speaker":"Patrick","startTime":533.37,"endTime":536.97,"body":"point that I proceeded to tell"},{"speaker":"Patrick","startTime":536.97,"endTime":541.05,"body":"an 11 minute story on tank"},{"speaker":"Patrick","startTime":536.97,"endTime":541.05,"body":"production during World War Two,"},{"speaker":"Patrick","startTime":541.32,"endTime":545.1,"body":"of which Greg, the entire thing,"},{"speaker":"Patrick","startTime":541.32,"endTime":545.1,"body":"I just thought it was very"},{"speaker":"Patrick","startTime":545.1,"endTime":548.82,"body":"important to clarify how"},{"speaker":"Patrick","startTime":545.1,"endTime":548.82,"body":"interesting that was, here's"},{"speaker":"Patrick","startTime":548.82,"endTime":553.65,"body":"your job, you are sent to a town"},{"speaker":"Patrick","startTime":548.82,"endTime":553.65,"body":"and your goal is to estimate how"},{"speaker":"Patrick","startTime":553.65,"endTime":558.09,"body":"many buses are on the street at"},{"speaker":"Patrick","startTime":553.65,"endTime":558.09,"body":"any given time. Now they send"},{"speaker":"Patrick","startTime":558.09,"endTime":561.72,"body":"out buses sequentially numbered"},{"speaker":"Patrick","startTime":558.09,"endTime":561.72,"body":"the first buses, one, the second"},{"speaker":"Patrick","startTime":561.72,"endTime":565.59,"body":"buses, two up to the number of"},{"speaker":"Patrick","startTime":561.72,"endTime":565.59,"body":"however many are out on the"},{"speaker":"Patrick","startTime":565.59,"endTime":569.61,"body":"street at a time. And you have"},{"speaker":"Patrick","startTime":565.59,"endTime":569.61,"body":"to here's the Calvin Ball, pick"},{"speaker":"Patrick","startTime":569.61,"endTime":574.14,"body":"the best guess for how many"},{"speaker":"Patrick","startTime":569.61,"endTime":574.14,"body":"total buses are on the street at"},{"speaker":"Patrick","startTime":574.14,"endTime":577.2,"body":"that moment. Here's the trick."},{"speaker":"Patrick","startTime":574.14,"endTime":577.2,"body":"You're only allowed to observe"},{"speaker":"Patrick","startTime":577.2,"endTime":581.07,"body":"one bus, you get a cup of"},{"speaker":"Patrick","startTime":577.2,"endTime":581.07,"body":"coffee, you sit on the bench,"},{"speaker":"Patrick","startTime":581.19,"endTime":586.89,"body":"and you wait for a bus to drive"},{"speaker":"Patrick","startTime":581.19,"endTime":586.89,"body":"by. And bus number 27 drives by"},{"speaker":"Patrick","startTime":587.1,"endTime":590.37,"body":"that's it, you're done. You have"},{"speaker":"Patrick","startTime":587.1,"endTime":590.37,"body":"your one observation. And the"},{"speaker":"Patrick","startTime":590.37,"endTime":594.51,"body":"challenge is estimate how many"},{"speaker":"Patrick","startTime":590.37,"endTime":594.51,"body":"buses are on the street, given"},{"speaker":"Patrick","startTime":594.54,"endTime":599.82,"body":"that you just observed 27 Well,"},{"speaker":"Patrick","startTime":594.54,"endTime":599.82,"body":"there are at least 27 That's"},{"speaker":"Patrick","startTime":599.82,"endTime":607.38,"body":"right. So the maximum likelihood"},{"speaker":"Patrick","startTime":599.82,"endTime":607.38,"body":"estimate in that scenario is 27."},{"speaker":"Patrick","startTime":608.85,"endTime":613.38,"body":"Why? Because the highest"},{"speaker":"Patrick","startTime":608.85,"endTime":613.38,"body":"probability that you would have"},{"speaker":"Patrick","startTime":613.38,"endTime":618.27,"body":"observed that bus is if there"},{"speaker":"Patrick","startTime":613.38,"endTime":618.27,"body":"were 27. On the street, there"},{"speaker":"Patrick","startTime":618.27,"endTime":623.67,"body":"was a 127 chance that you would"},{"speaker":"Patrick","startTime":618.27,"endTime":623.67,"body":"have observed that bus. If there"},{"speaker":"Patrick","startTime":623.67,"endTime":630.54,"body":"were 54 buses and 27 drove by,"},{"speaker":"Patrick","startTime":623.67,"endTime":630.54,"body":"there was a 1/54 chance that you"},{"speaker":"Patrick","startTime":630.54,"endTime":633.57,"body":"would have observed that bus. So"},{"speaker":"Patrick","startTime":630.54,"endTime":633.57,"body":"you would have picked a value"},{"speaker":"Patrick","startTime":633.57,"endTime":637.86,"body":"that made it less likely that"},{"speaker":"Patrick","startTime":633.57,"endTime":637.86,"body":"you would have observed that"},{"speaker":"Patrick","startTime":637.86,"endTime":643.23,"body":"sample data. I really love that,"},{"speaker":"Patrick","startTime":637.86,"endTime":643.23,"body":"how do we select an estimate of"},{"speaker":"Patrick","startTime":643.23,"endTime":648.27,"body":"an unknown parameter that"},{"speaker":"Patrick","startTime":643.23,"endTime":648.27,"body":"maximizes the likelihood that we"},{"speaker":"Patrick","startTime":648.27,"endTime":650.88,"body":"would have observed our sample"},{"speaker":"Patrick","startTime":648.27,"endTime":650.88,"body":"data? Yeah,"},{"speaker":"Greg","startTime":650.91,"endTime":654.75,"body":"what you just said is"},{"speaker":"Greg","startTime":650.91,"endTime":654.75,"body":"perfect. That whole flipping of"},{"speaker":"Greg","startTime":654.75,"endTime":658.2,"body":"things on its head is at the"},{"speaker":"Greg","startTime":654.75,"endTime":658.2,"body":"core of maximum likelihood."},{"speaker":"Greg","startTime":658.41,"endTime":662.52,"body":"We're so accustomed in the way"},{"speaker":"Greg","startTime":658.41,"endTime":662.52,"body":"we talk about things to say"},{"speaker":"Greg","startTime":662.55,"endTime":665.58,"body":"these are the characteristics of"},{"speaker":"Greg","startTime":662.55,"endTime":665.58,"body":"the population, for example,"},{"speaker":"Greg","startTime":665.82,"endTime":669.54,"body":"there is this mean, and there's"},{"speaker":"Greg","startTime":665.82,"endTime":669.54,"body":"this variance. And we talk about"},{"speaker":"Greg","startTime":669.54,"endTime":672.21,"body":"what is the probability"},{"speaker":"Greg","startTime":669.54,"endTime":672.21,"body":"associated with a particular"},{"speaker":"Greg","startTime":672.21,"endTime":676.71,"body":"observation. And this just"},{"speaker":"Greg","startTime":672.21,"endTime":676.71,"body":"completely flips it? So so"},{"speaker":"Greg","startTime":676.71,"endTime":681.03,"body":"cleverly that now we say, we"},{"speaker":"Greg","startTime":676.71,"endTime":681.03,"body":"have observed these data? What"},{"speaker":"Greg","startTime":681.03,"endTime":685.02,"body":"would the configuration of the"},{"speaker":"Greg","startTime":681.03,"endTime":685.02,"body":"population have to be like for"},{"speaker":"Greg","startTime":685.05,"endTime":689.13,"body":"our observations to have the"},{"speaker":"Greg","startTime":685.05,"endTime":689.13,"body":"maximum likelihood of having"},{"speaker":"Greg","startTime":689.13,"endTime":693.78,"body":"occurred? So when you talk about"},{"speaker":"Greg","startTime":689.13,"endTime":693.78,"body":"seeing bus number 27, the"},{"speaker":"Greg","startTime":693.81,"endTime":697.56,"body":"configuration for the population"},{"speaker":"Greg","startTime":693.81,"endTime":697.56,"body":"would not be that there are 1000"},{"speaker":"Greg","startTime":697.56,"endTime":701.58,"body":"buses, because the likelihood of"},{"speaker":"Greg","startTime":697.56,"endTime":701.58,"body":"observing bus number 27, would"},{"speaker":"Greg","startTime":701.58,"endTime":704.7,"body":"have been so small. So at the"},{"speaker":"Greg","startTime":701.58,"endTime":704.7,"body":"crux of maximum likelihood is"},{"speaker":"Greg","startTime":704.7,"endTime":707.25,"body":"figuring out what would the"},{"speaker":"Greg","startTime":704.7,"endTime":707.25,"body":"population have to look like so"},{"speaker":"Greg","startTime":707.25,"endTime":710.37,"body":"that the observations we have in"},{"speaker":"Greg","startTime":707.25,"endTime":710.37,"body":"our hand have the maximum"},{"speaker":"Greg","startTime":710.37,"endTime":713.91,"body":"likelihood. And that was this"},{"speaker":"Greg","startTime":710.37,"endTime":713.91,"body":"beautiful flip that the young ra"},{"speaker":"Greg","startTime":713.91,"endTime":718.11,"body":"Fisher Ronald Rani, as I'm sure"},{"speaker":"Greg","startTime":713.91,"endTime":718.11,"body":"they called him, had this"},{"speaker":"Greg","startTime":718.11,"endTime":719.79,"body":"insight into how to think about"},{"speaker":"Greg","startTime":718.11,"endTime":719.79,"body":"things."},{"speaker":"Patrick","startTime":719.849,"endTime":723.809,"body":"And it does introduce a"},{"speaker":"Patrick","startTime":719.849,"endTime":723.809,"body":"point of confusion of the use of"},{"speaker":"Patrick","startTime":723.809,"endTime":728.009,"body":"the word probability and the use"},{"speaker":"Patrick","startTime":723.809,"endTime":728.009,"body":"of the word likelihood, because"},{"speaker":"Patrick","startTime":728.009,"endTime":730.499,"body":"you were very careful in your"},{"speaker":"Patrick","startTime":728.009,"endTime":730.499,"body":"language right there and very"},{"speaker":"Patrick","startTime":730.499,"endTime":735.299,"body":"appropriately. So if I give you"},{"speaker":"Patrick","startTime":730.499,"endTime":735.299,"body":"a mean and a variance, and then"},{"speaker":"Patrick","startTime":735.299,"endTime":739.439,"body":"talk to you about what is the"},{"speaker":"Patrick","startTime":735.299,"endTime":739.439,"body":"probability of randomly drawn"},{"speaker":"Patrick","startTime":739.439,"endTime":742.619,"body":"score will be above this, or"},{"speaker":"Patrick","startTime":739.439,"endTime":742.619,"body":"below that or in between these"},{"speaker":"Patrick","startTime":742.619,"endTime":748.139,"body":"two values? Typically, we talked"},{"speaker":"Patrick","startTime":742.619,"endTime":748.139,"body":"about that as probability. Here,"},{"speaker":"Patrick","startTime":748.169,"endTime":752.639,"body":"we're going to use a different"},{"speaker":"Patrick","startTime":748.169,"endTime":752.639,"body":"terminology, which is, what"},{"speaker":"Patrick","startTime":752.639,"endTime":758.849,"body":"value of mean and variance"},{"speaker":"Patrick","startTime":752.639,"endTime":758.849,"body":"maximizes the likelihood of the"},{"speaker":"Patrick","startTime":758.849,"endTime":763.619,"body":"data that we observed. So we"},{"speaker":"Patrick","startTime":758.849,"endTime":763.619,"body":"already have the data. And we're"},{"speaker":"Patrick","startTime":763.619,"endTime":768.059,"body":"talking about what values of"},{"speaker":"Patrick","startTime":763.619,"endTime":768.059,"body":"these estimates would make this"},{"speaker":"Patrick","startTime":768.059,"endTime":773.069,"body":"set of data most likely that we"},{"speaker":"Patrick","startTime":768.059,"endTime":773.069,"body":"observed and that is that same"},{"speaker":"Patrick","startTime":773.069,"endTime":777.779,"body":"thing with the bus, what number"},{"speaker":"Patrick","startTime":773.069,"endTime":777.779,"body":"of total buses would maximize"},{"speaker":"Patrick","startTime":777.779,"endTime":782.249,"body":"the likelihood that you saw that"},{"speaker":"Patrick","startTime":777.779,"endTime":782.249,"body":"bus, and it's 120 summit."},{"speaker":"Greg","startTime":782.579,"endTime":784.529,"body":"Now, given that we don't"},{"speaker":"Greg","startTime":782.579,"endTime":784.529,"body":"have a ton of listeners who are"},{"speaker":"Greg","startTime":784.529,"endTime":788.879,"body":"in the bus sciences, let's"},{"speaker":"Greg","startTime":784.529,"endTime":788.879,"body":"translate this into things that"},{"speaker":"Greg","startTime":788.879,"endTime":792.329,"body":"people think about and maybe"},{"speaker":"Greg","startTime":788.879,"endTime":792.329,"body":"start with a set of scores. They"},{"speaker":"Greg","startTime":792.329,"endTime":796.679,"body":"could be heights, they could be"},{"speaker":"Greg","startTime":792.329,"endTime":796.679,"body":"scores on a test, we think about"},{"speaker":"Greg","startTime":796.679,"endTime":800.099,"body":"this in the univariate"},{"speaker":"Greg","startTime":796.679,"endTime":800.099,"body":"situation, how do we translate"},{"speaker":"Greg","startTime":800.099,"endTime":801.869,"body":"this into the maximum likelihood"},{"speaker":"Greg","startTime":800.099,"endTime":801.869,"body":"world?"},{"speaker":"Patrick","startTime":801.989,"endTime":806.429,"body":"Okay, let me ask how"},{"speaker":"Patrick","startTime":801.989,"endTime":806.429,"body":"you teach something. Because I"},{"speaker":"Patrick","startTime":806.429,"endTime":810.839,"body":"think anybody who ever teaches"},{"speaker":"Patrick","startTime":806.429,"endTime":810.839,"body":"this has to wrestle with this"},{"speaker":"Patrick","startTime":810.839,"endTime":814.049,"body":"issue, we're going to talk about"},{"speaker":"Patrick","startTime":810.839,"endTime":814.049,"body":"a univariate normal"},{"speaker":"Patrick","startTime":814.049,"endTime":817.349,"body":"distribution. And much of what"},{"speaker":"Patrick","startTime":814.049,"endTime":817.349,"body":"we talked about today is going"},{"speaker":"Patrick","startTime":817.349,"endTime":821.279,"body":"to relate to naturally normal"},{"speaker":"Patrick","startTime":817.349,"endTime":821.279,"body":"theory, maximum likelihood, it"},{"speaker":"Patrick","startTime":821.279,"endTime":823.799,"body":"turns out, we don't have to do"},{"speaker":"Patrick","startTime":821.279,"endTime":823.799,"body":"that there are other ways we can"},{"speaker":"Patrick","startTime":823.799,"endTime":827.369,"body":"go about doing it. But we are"},{"speaker":"Patrick","startTime":823.799,"endTime":827.369,"body":"going to assume this normal"},{"speaker":"Patrick","startTime":827.369,"endTime":831.929,"body":"distribution, all of us have"},{"speaker":"Patrick","startTime":827.369,"endTime":831.929,"body":"seen this beautiful expression"},{"speaker":"Patrick","startTime":831.959,"endTime":838.589,"body":"for that one over sigma root two"},{"speaker":"Patrick","startTime":831.959,"endTime":838.589,"body":"pi e to the negative z squared"},{"speaker":"Patrick","startTime":838.589,"endTime":842.609,"body":"over two. Nice. Now what that"},{"speaker":"Patrick","startTime":838.589,"endTime":842.609,"body":"does is it's just like a line,"},{"speaker":"Patrick","startTime":842.699,"endTime":846.539,"body":"where if you have a plus Bx and"},{"speaker":"Patrick","startTime":842.699,"endTime":846.539,"body":"you drop in points across X, and"},{"speaker":"Patrick","startTime":846.539,"endTime":849.869,"body":"it draws a line, this is exactly"},{"speaker":"Patrick","startTime":846.539,"endTime":849.869,"body":"the same, it's a sausage maker,"},{"speaker":"Patrick","startTime":850.229,"endTime":854.429,"body":"and you drop in values of x in"},{"speaker":"Patrick","startTime":850.229,"endTime":854.429,"body":"it draws out this beautiful"},{"speaker":"Patrick","startTime":854.429,"endTime":858.119,"body":"normal distribution. Alright, so"},{"speaker":"Patrick","startTime":854.429,"endTime":858.119,"body":"here's my question for you. You"},{"speaker":"Patrick","startTime":858.119,"endTime":864.689,"body":"drop a particular value in crank"},{"speaker":"Patrick","startTime":858.119,"endTime":864.689,"body":"it, and it gives you a specific"},{"speaker":"Patrick","startTime":864.689,"endTime":869.609,"body":"numerical value, which is the"},{"speaker":"Patrick","startTime":864.689,"endTime":869.609,"body":"height of the normal curve at"},{"speaker":"Patrick","startTime":869.639,"endTime":873.779,"body":"that point? How do you define"},{"speaker":"Patrick","startTime":869.639,"endTime":873.779,"body":"what that is to your class?"},{"speaker":"Greg","startTime":873.869,"endTime":876.839,"body":"Yeah, I certainly don't"},{"speaker":"Greg","startTime":873.869,"endTime":876.839,"body":"refer to it as a probability."},{"speaker":"Greg","startTime":876.899,"endTime":881.579,"body":"Nope. I talked about that value"},{"speaker":"Greg","startTime":876.899,"endTime":881.579,"body":"as being likelihood. And one of"},{"speaker":"Greg","startTime":881.579,"endTime":885.539,"body":"the reasons is that if you think"},{"speaker":"Greg","startTime":881.579,"endTime":885.539,"body":"about a normal curve, or"},{"speaker":"Greg","startTime":885.539,"endTime":889.889,"body":"frankly, any curve in order to"},{"speaker":"Greg","startTime":885.539,"endTime":889.889,"body":"amass a certain amount of"},{"speaker":"Greg","startTime":889.919,"endTime":893.609,"body":"probability, we usually have to"},{"speaker":"Greg","startTime":889.919,"endTime":893.609,"body":"frame an interval associated"},{"speaker":"Greg","startTime":893.609,"endTime":897.089,"body":"with it so that we can take the"},{"speaker":"Greg","startTime":893.609,"endTime":897.089,"body":"area under that curve and say,"},{"speaker":"Greg","startTime":897.089,"endTime":900.329,"body":"how much of the area under the"},{"speaker":"Greg","startTime":897.089,"endTime":900.329,"body":"curve are we talking about? If I"},{"speaker":"Greg","startTime":900.359,"endTime":904.439,"body":"give you a specific point and"},{"speaker":"Greg","startTime":900.359,"endTime":904.439,"body":"say, how much area under the"},{"speaker":"Greg","startTime":904.439,"endTime":909.149,"body":"curve does the number 14 Point"},{"speaker":"Greg","startTime":904.439,"endTime":909.149,"body":"to occupy, unless you assign the"},{"speaker":"Greg","startTime":909.149,"endTime":913.319,"body":"number 14 point to an interval,"},{"speaker":"Greg","startTime":909.149,"endTime":913.319,"body":"like an interval that goes down"},{"speaker":"Greg","startTime":913.319,"endTime":916.469,"body":"to a little bit below 14.2, and"},{"speaker":"Greg","startTime":913.319,"endTime":916.469,"body":"a little bit above, it's very"},{"speaker":"Greg","startTime":916.469,"endTime":918.689,"body":"hard to talk about that"},{"speaker":"Greg","startTime":916.469,"endTime":918.689,"body":"probabilistically. But of"},{"speaker":"Greg","startTime":918.689,"endTime":921.659,"body":"course, when you drop 14.2, in"},{"speaker":"Greg","startTime":918.689,"endTime":921.659,"body":"the sausage maker, it will still"},{"speaker":"Greg","startTime":921.659,"endTime":925.259,"body":"tell you how tall the curve is"},{"speaker":"Greg","startTime":921.659,"endTime":925.259,"body":"above it. But it really isn't in"},{"speaker":"Greg","startTime":925.259,"endTime":927.989,"body":"a metric that we would call"},{"speaker":"Greg","startTime":925.259,"endTime":927.989,"body":"probability. It's related to"},{"speaker":"Greg","startTime":927.989,"endTime":931.079,"body":"probability. But I will use the"},{"speaker":"Greg","startTime":927.989,"endTime":931.079,"body":"term likelihood associated with"},{"speaker":"Greg","startTime":931.079,"endTime":932.069,"body":"that. Yep, exactly."},{"speaker":"Patrick","startTime":932.1,"endTime":935.43,"body":"That's the value of the"},{"speaker":"Patrick","startTime":932.1,"endTime":935.43,"body":"likelihood. Let me give you a"},{"speaker":"Patrick","startTime":935.43,"endTime":940.59,"body":"pop quiz. What is the"},{"speaker":"Patrick","startTime":935.43,"endTime":940.59,"body":"probability of a fair coin"},{"speaker":"Patrick","startTime":940.68,"endTime":944.31,"body":"getting a heads point five? What"},{"speaker":"Patrick","startTime":940.68,"endTime":944.31,"body":"is the probability of getting"},{"speaker":"Patrick","startTime":944.34,"endTime":947.04,"body":"two heads in a row on that fair"},{"speaker":"Patrick","startTime":944.34,"endTime":947.04,"body":"coin,"},{"speaker":"Greg","startTime":947.1,"endTime":949.71,"body":"point five times point"},{"speaker":"Greg","startTime":947.1,"endTime":949.71,"body":"five, because they're"},{"speaker":"Greg","startTime":949.71,"endTime":952.2,"body":"independent events, point two,"},{"speaker":"Greg","startTime":949.71,"endTime":952.2,"body":"five. All right, so"},{"speaker":"Patrick","startTime":952.2,"endTime":955.29,"body":"you did two things to"},{"speaker":"Patrick","startTime":952.2,"endTime":955.29,"body":"that I was after you multiplied"},{"speaker":"Patrick","startTime":955.29,"endTime":958.8,"body":"the individual probabilities."},{"speaker":"Patrick","startTime":955.29,"endTime":958.8,"body":"And you assumed that they were"},{"speaker":"Patrick","startTime":958.8,"endTime":963.06,"body":"independent, what that allows"},{"speaker":"Patrick","startTime":958.8,"endTime":963.06,"body":"is, we can get the joint"},{"speaker":"Patrick","startTime":963.06,"endTime":966.09,"body":"probability of those two events"},{"speaker":"Patrick","startTime":963.06,"endTime":966.09,"body":"because they are independent"},{"speaker":"Patrick","startTime":966.09,"endTime":968.79,"body":"from one another, whether you"},{"speaker":"Patrick","startTime":966.09,"endTime":968.79,"body":"get heads or a tail on the first"},{"speaker":"Patrick","startTime":968.79,"endTime":971.49,"body":"one has no bearing on whether"},{"speaker":"Patrick","startTime":968.79,"endTime":971.49,"body":"you get a heads or a tail. And"},{"speaker":"Patrick","startTime":971.49,"endTime":975.93,"body":"the second one, we can apply"},{"speaker":"Patrick","startTime":971.49,"endTime":975.93,"body":"that same principle to taking"},{"speaker":"Patrick","startTime":975.93,"endTime":981.18,"body":"these individual likelihoods."},{"speaker":"Patrick","startTime":975.93,"endTime":981.18,"body":"But for a set of observations,"},{"speaker":"Patrick","startTime":981.18,"endTime":985.17,"body":"compute the individual"},{"speaker":"Patrick","startTime":981.18,"endTime":985.17,"body":"likelihoods. And if they are"},{"speaker":"Patrick","startTime":985.17,"endTime":990.84,"body":"independent, we can take the"},{"speaker":"Patrick","startTime":985.17,"endTime":990.84,"body":"product of those likelihoods and"},{"speaker":"Patrick","startTime":990.84,"endTime":995.28,"body":"get an overall value that"},{"speaker":"Patrick","startTime":990.84,"endTime":995.28,"body":"represents the likelihood for"},{"speaker":"Patrick","startTime":995.28,"endTime":997.71,"body":"the set of observations. I love"},{"speaker":"Greg","startTime":997.71,"endTime":1000.5,"body":"that. So if you had a"},{"speaker":"Greg","startTime":997.71,"endTime":1000.5,"body":"group of people standing on a"},{"speaker":"Greg","startTime":1000.5,"endTime":1004.55,"body":"number line, and you put this"},{"speaker":"Greg","startTime":1000.5,"endTime":1004.55,"body":"curve over their heads, the"},{"speaker":"Greg","startTime":1004.55,"endTime":1008.06,"body":"people who look up and it's a"},{"speaker":"Greg","startTime":1004.55,"endTime":1008.06,"body":"long way to the top"},{"speaker":"Greg","startTime":1013.07,"endTime":1015.5,"body":"Those are people are standing in"},{"speaker":"Greg","startTime":1013.07,"endTime":1015.5,"body":"a place, that's very, very"},{"speaker":"Greg","startTime":1015.5,"endTime":1018.98,"body":"likely. And if someone is"},{"speaker":"Greg","startTime":1015.5,"endTime":1018.98,"body":"standing out near the tails,"},{"speaker":"Greg","startTime":1018.98,"endTime":1022.28,"body":"they look up and that curve is"},{"speaker":"Greg","startTime":1018.98,"endTime":1022.28,"body":"crashing down on them, they have"},{"speaker":"Greg","startTime":1022.28,"endTime":1025.67,"body":"a value that is not particularly"},{"speaker":"Greg","startTime":1022.28,"endTime":1025.67,"body":"likely. So things toward the"},{"speaker":"Greg","startTime":1025.67,"endTime":1028.16,"body":"higher parts of the curve are"},{"speaker":"Greg","startTime":1025.67,"endTime":1028.16,"body":"more likely things out toward"},{"speaker":"Greg","startTime":1028.16,"endTime":1031.97,"body":"the answer less likely. And when"},{"speaker":"Greg","startTime":1028.16,"endTime":1031.97,"body":"you multiply a bunch of things,"},{"speaker":"Greg","startTime":1032.0,"endTime":1036.95,"body":"it will be really big if a lot"},{"speaker":"Greg","startTime":1032.0,"endTime":1036.95,"body":"of people have those high values"},{"speaker":"Greg","startTime":1036.95,"endTime":1040.55,"body":"of the curve above them. And it"},{"speaker":"Greg","startTime":1036.95,"endTime":1040.55,"body":"will be really small if a lot of"},{"speaker":"Greg","startTime":1040.55,"endTime":1043.34,"body":"people have really small values"},{"speaker":"Greg","startTime":1040.55,"endTime":1043.34,"body":"of that curve above them."},{"speaker":"Patrick","startTime":1043.55,"endTime":1046.01,"body":"Alright, so let's say"},{"speaker":"Patrick","startTime":1043.55,"endTime":1046.01,"body":"we have five observations, let's"},{"speaker":"Patrick","startTime":1046.01,"endTime":1048.32,"body":"go to your people, right on the"},{"speaker":"Patrick","startTime":1046.01,"endTime":1048.32,"body":"number line, you have five"},{"speaker":"Patrick","startTime":1048.32,"endTime":1050.24,"body":"different people in there"},{"speaker":"Patrick","startTime":1048.32,"endTime":1050.24,"body":"scattered on the number line,"},{"speaker":"Patrick","startTime":1050.72,"endTime":1054.77,"body":"we're going to start super"},{"speaker":"Patrick","startTime":1050.72,"endTime":1054.77,"body":"simple, we are going to somehow"},{"speaker":"Patrick","startTime":1054.8,"endTime":1056.99,"body":"know what the variance is. And"},{"speaker":"Patrick","startTime":1054.8,"endTime":1056.99,"body":"we're going to hold that"},{"speaker":"Patrick","startTime":1056.99,"endTime":1061.22,"body":"constant. So picture just a"},{"speaker":"Patrick","startTime":1056.99,"endTime":1061.22,"body":"normal distribution, we are"},{"speaker":"Patrick","startTime":1061.22,"endTime":1064.37,"body":"going to slide it up and down,"},{"speaker":"Patrick","startTime":1061.22,"endTime":1064.37,"body":"we're not going to move the"},{"speaker":"Patrick","startTime":1064.37,"endTime":1067.7,"body":"people we're going to move the"},{"speaker":"Patrick","startTime":1064.37,"endTime":1067.7,"body":"curve. Oh, that's so important."},{"speaker":"Patrick","startTime":1067.79,"endTime":1071.57,"body":"I am going to start by rage"},{"speaker":"Patrick","startTime":1067.79,"endTime":1071.57,"body":"hooking it. And then I'm going"},{"speaker":"Patrick","startTime":1071.57,"endTime":1077.69,"body":"to let you sexy whole kit. All"},{"speaker":"Patrick","startTime":1071.57,"endTime":1077.69,"body":"right. I'm gonna rage HK and I'm"},{"speaker":"Patrick","startTime":1077.69,"endTime":1080.66,"body":"just going to randomly drop it"},{"speaker":"Patrick","startTime":1077.69,"endTime":1080.66,"body":"down over the five, throw it"},{"speaker":"Patrick","startTime":1080.66,"endTime":1083.72,"body":"down. Yep, just throw it down."},{"speaker":"Patrick","startTime":1080.66,"endTime":1083.72,"body":"And let's see where we start."},{"speaker":"Patrick","startTime":1084.32,"endTime":1087.02,"body":"Well, what I'm going to do is"},{"speaker":"Patrick","startTime":1084.32,"endTime":1087.02,"body":"that normal distribution, that's"},{"speaker":"Patrick","startTime":1087.02,"endTime":1090.17,"body":"going to be somewhere over the"},{"speaker":"Patrick","startTime":1087.02,"endTime":1090.17,"body":"five cases, I'm going to take"},{"speaker":"Patrick","startTime":1090.2,"endTime":1094.61,"body":"each case and go up to where"},{"speaker":"Patrick","startTime":1090.2,"endTime":1094.61,"body":"their observation intersects the"},{"speaker":"Patrick","startTime":1094.61,"endTime":1097.07,"body":"curve. And that is their"},{"speaker":"Patrick","startTime":1094.61,"endTime":1097.07,"body":"likelihood. And I'm going to"},{"speaker":"Patrick","startTime":1097.07,"endTime":1100.37,"body":"write down all five of them. And"},{"speaker":"Patrick","startTime":1097.07,"endTime":1100.37,"body":"I'm going to multiply all five"},{"speaker":"Patrick","startTime":1100.37,"endTime":1103.79,"body":"of them. And I'm going to get"},{"speaker":"Patrick","startTime":1100.37,"endTime":1103.79,"body":"some product of those five"},{"speaker":"Patrick","startTime":1103.79,"endTime":1107.09,"body":"likelihoods it's going to be"},{"speaker":"Patrick","startTime":1103.79,"endTime":1107.09,"body":"some value, whatever. And then"},{"speaker":"Patrick","startTime":1107.09,"endTime":1112.76,"body":"rage HK is going to grunt and"},{"speaker":"Patrick","startTime":1107.09,"endTime":1112.76,"body":"move the curve over a little bit"},{"speaker":"Patrick","startTime":1112.85,"endTime":1116.3,"body":"and redo it, and the product of"},{"speaker":"Patrick","startTime":1112.85,"endTime":1116.3,"body":"those likelihoods. It's actually"},{"speaker":"Patrick","startTime":1116.3,"endTime":1120.35,"body":"smaller than the first one."},{"speaker":"Patrick","startTime":1116.3,"endTime":1120.35,"body":"Alright, so that's less likely."},{"speaker":"Patrick","startTime":1120.68,"endTime":1124.79,"body":"And Rachel grunts and pulls it"},{"speaker":"Patrick","startTime":1120.68,"endTime":1124.79,"body":"the other way. And now it's"},{"speaker":"Patrick","startTime":1124.79,"endTime":1127.85,"body":"bigger and moves it left and"},{"speaker":"Patrick","startTime":1124.79,"endTime":1127.85,"body":"moves it right and moves it into"},{"speaker":"Patrick","startTime":1127.85,"endTime":1135.29,"body":"rage Hulk is raging and moves"},{"speaker":"Patrick","startTime":1127.85,"endTime":1135.29,"body":"this intel, it's not changing"},{"speaker":"Patrick","startTime":1135.29,"endTime":1140.0,"body":"very much around the largest"},{"speaker":"Patrick","startTime":1135.29,"endTime":1140.0,"body":"value possible. And then range"},{"speaker":"Patrick","startTime":1140.0,"endTime":1145.79,"body":"hope grunts and stops. And the"},{"speaker":"Patrick","startTime":1140.0,"endTime":1145.79,"body":"mode of that distribution"},{"speaker":"Patrick","startTime":1145.82,"endTime":1150.41,"body":"defines the center of the"},{"speaker":"Patrick","startTime":1145.82,"endTime":1150.41,"body":"distribution that maximizes the"},{"speaker":"Patrick","startTime":1150.41,"endTime":1156.32,"body":"likelihood of observing those"},{"speaker":"Patrick","startTime":1150.41,"endTime":1156.32,"body":"five cases. Now sexy Hulk me"},{"speaker":"Greg","startTime":1158.12,"endTime":1161.84,"body":"about rage Hulk by the"},{"speaker":"Greg","startTime":1158.12,"endTime":1161.84,"body":"way, rage Hulk stopped at some"},{"speaker":"Greg","startTime":1161.84,"endTime":1164.69,"body":"point moving that thing to the"},{"speaker":"Greg","startTime":1161.84,"endTime":1164.69,"body":"left into the right, right,"},{"speaker":"Greg","startTime":1164.69,"endTime":1168.98,"body":"Rachel was tired. But then sexy"},{"speaker":"Greg","startTime":1164.69,"endTime":1168.98,"body":"Hulk comes in and pushes up his"},{"speaker":"Greg","startTime":1168.98,"endTime":1172.76,"body":"glasses and says it is a"},{"speaker":"Greg","startTime":1168.98,"endTime":1172.76,"body":"calculus problem where you can"},{"speaker":"Greg","startTime":1172.76,"endTime":1176.0,"body":"take the formula for the normal"},{"speaker":"Greg","startTime":1172.76,"endTime":1176.0,"body":"distribution and the"},{"speaker":"Greg","startTime":1176.0,"endTime":1180.29,"body":"observations that you have. And"},{"speaker":"Greg","startTime":1176.0,"endTime":1180.29,"body":"you can actually derive what is"},{"speaker":"Greg","startTime":1180.32,"endTime":1184.73,"body":"the population value for the"},{"speaker":"Greg","startTime":1180.32,"endTime":1184.73,"body":"mean given a particular variance"},{"speaker":"Greg","startTime":1185.33,"endTime":1188.9,"body":"that would maximize the"},{"speaker":"Greg","startTime":1185.33,"endTime":1188.9,"body":"likelihood of these five"},{"speaker":"Greg","startTime":1188.9,"endTime":1192.53,"body":"observations. And if we go"},{"speaker":"Greg","startTime":1188.9,"endTime":1192.53,"body":"through the calculus of it, we"},{"speaker":"Greg","startTime":1192.53,"endTime":1196.16,"body":"don't just beat on this normal"},{"speaker":"Greg","startTime":1192.53,"endTime":1196.16,"body":"curve left and right. What we do"},{"speaker":"Greg","startTime":1196.19,"endTime":1202.37,"body":"is we take the derivative we say"},{"speaker":"Greg","startTime":1196.19,"endTime":1202.37,"body":"At the derivative equal to zero,"},{"speaker":"Greg","startTime":1202.49,"endTime":1206.69,"body":"and we're looking for the value,"},{"speaker":"Greg","startTime":1202.49,"endTime":1206.69,"body":"whatever it is of mu that"},{"speaker":"Greg","startTime":1206.69,"endTime":1210.23,"body":"maximizes this particular"},{"speaker":"Greg","startTime":1206.69,"endTime":1210.23,"body":"function. And through calculus,"},{"speaker":"Greg","startTime":1210.32,"endTime":1214.49,"body":"derivatives, all of that stuff,"},{"speaker":"Greg","startTime":1210.32,"endTime":1214.49,"body":"it comes out just so beautifully"},{"speaker":"Greg","startTime":1214.7,"endTime":1219.8,"body":"sexy Hulk has big tears flowing"},{"speaker":"Greg","startTime":1214.7,"endTime":1219.8,"body":"down his green face. And the"},{"speaker":"Greg","startTime":1219.8,"endTime":1224.39,"body":"sample mean, as we know, it is"},{"speaker":"Greg","startTime":1219.8,"endTime":1224.39,"body":"the maximum likelihood estimator"},{"speaker":"Greg","startTime":1224.39,"endTime":1227.75,"body":"of that best possible central"},{"speaker":"Greg","startTime":1224.39,"endTime":1227.75,"body":"location for the normal"},{"speaker":"Greg","startTime":1227.75,"endTime":1228.44,"body":"distribution."},{"speaker":"Patrick","startTime":1228.62,"endTime":1231.2,"body":"And what you"},{"speaker":"Patrick","startTime":1228.62,"endTime":1231.2,"body":"wonderfully described in terms"},{"speaker":"Patrick","startTime":1231.2,"endTime":1234.74,"body":"of derivatives and setting them"},{"speaker":"Patrick","startTime":1231.2,"endTime":1234.74,"body":"to zero and solving. We talked"},{"speaker":"Patrick","startTime":1234.74,"endTime":1237.62,"body":"about last week for the ordinary"},{"speaker":"Patrick","startTime":1234.74,"endTime":1237.62,"body":"least squares, it's right, and"},{"speaker":"Patrick","startTime":1237.62,"endTime":1242.57,"body":"it's a very similar criterion."},{"speaker":"Patrick","startTime":1237.62,"endTime":1242.57,"body":"It's just a different Calvin"},{"speaker":"Patrick","startTime":1242.57,"endTime":1247.28,"body":"Ball rule. So last week, we said"},{"speaker":"Patrick","startTime":1242.57,"endTime":1247.28,"body":"we're going to pick the values"},{"speaker":"Patrick","startTime":1247.37,"endTime":1251.81,"body":"of the intercept and slope of a"},{"speaker":"Patrick","startTime":1247.37,"endTime":1251.81,"body":"regression line that minimizes"},{"speaker":"Patrick","startTime":1251.81,"endTime":1255.11,"body":"the sum of the squared"},{"speaker":"Patrick","startTime":1251.81,"endTime":1255.11,"body":"residuals, we described, it"},{"speaker":"Patrick","startTime":1255.2,"endTime":1259.25,"body":"sketches out this beautiful"},{"speaker":"Patrick","startTime":1255.2,"endTime":1259.25,"body":"parabola, and rage, HK says,"},{"speaker":"Patrick","startTime":1259.25,"endTime":1262.31,"body":"what about this? What about"},{"speaker":"Patrick","startTime":1259.25,"endTime":1262.31,"body":"this, what about this, and we"},{"speaker":"Patrick","startTime":1262.31,"endTime":1267.11,"body":"fill in a parabola, and sexy"},{"speaker":"Patrick","startTime":1262.31,"endTime":1267.11,"body":"Hulk says, I can write an"},{"speaker":"Patrick","startTime":1267.11,"endTime":1271.22,"body":"equation for that the first"},{"speaker":"Patrick","startTime":1267.11,"endTime":1271.22,"body":"derivative that equals zero is"},{"speaker":"Patrick","startTime":1271.22,"endTime":1274.76,"body":"the bottom of that trajectory."},{"speaker":"Patrick","startTime":1271.22,"endTime":1274.76,"body":"And that's going to be my best"},{"speaker":"Patrick","startTime":1274.76,"endTime":1278.69,"body":"estimate, for least squares,"},{"speaker":"Patrick","startTime":1274.76,"endTime":1278.69,"body":"we're doing a very, very similar"},{"speaker":"Patrick","startTime":1278.69,"endTime":1283.22,"body":"thing here. But now we're"},{"speaker":"Patrick","startTime":1278.69,"endTime":1283.22,"body":"changing best to what is the"},{"speaker":"Patrick","startTime":1283.22,"endTime":1287.9,"body":"point for our estimator that"},{"speaker":"Patrick","startTime":1283.22,"endTime":1287.9,"body":"maximizes the likelihood that we"},{"speaker":"Patrick","startTime":1287.9,"endTime":1291.47,"body":"would have observed our sample"},{"speaker":"Patrick","startTime":1287.9,"endTime":1291.47,"body":"data. So we're doing a very"},{"speaker":"Patrick","startTime":1291.47,"endTime":1294.98,"body":"similar kind of thing. But just"},{"speaker":"Patrick","startTime":1291.47,"endTime":1294.98,"body":"with a different criterion,"},{"speaker":"Patrick","startTime":1295.13,"endTime":1298.25,"body":"instead of minimizing the sum of"},{"speaker":"Patrick","startTime":1295.13,"endTime":1298.25,"body":"the squared residuals, we're"},{"speaker":"Patrick","startTime":1298.25,"endTime":1301.28,"body":"going to maximize the likelihood"},{"speaker":"Patrick","startTime":1298.25,"endTime":1301.28,"body":"that we would have observed our"},{"speaker":"Patrick","startTime":1301.28,"endTime":1302.06,"body":"sample data"},{"speaker":"Greg","startTime":1302.12,"endTime":1305.51,"body":"exactly. That is how"},{"speaker":"Greg","startTime":1302.12,"endTime":1305.51,"body":"maximum likelihood works. And"},{"speaker":"Greg","startTime":1305.51,"endTime":1309.11,"body":"we're talking about it right now"},{"speaker":"Greg","startTime":1305.51,"endTime":1309.11,"body":"in one dimension, but it extends"},{"speaker":"Greg","startTime":1309.11,"endTime":1312.14,"body":"to dealing with other things in"},{"speaker":"Greg","startTime":1309.11,"endTime":1312.14,"body":"one dimension, like the"},{"speaker":"Greg","startTime":1312.14,"endTime":1315.38,"body":"variance, and then multiple"},{"speaker":"Greg","startTime":1312.14,"endTime":1315.38,"body":"dimensions itself."},{"speaker":"Patrick","startTime":1315.44,"endTime":1318.38,"body":"If you've taken a"},{"speaker":"Patrick","startTime":1315.44,"endTime":1318.38,"body":"multivariate class, especially a"},{"speaker":"Patrick","startTime":1318.38,"endTime":1323.27,"body":"matrix based one, it is so"},{"speaker":"Patrick","startTime":1318.38,"endTime":1323.27,"body":"elegant in how you can take that"},{"speaker":"Patrick","startTime":1323.27,"endTime":1327.71,"body":"univariate distribution function"},{"speaker":"Patrick","startTime":1323.27,"endTime":1327.71,"body":"that we just describe the one"},{"speaker":"Patrick","startTime":1327.71,"endTime":1331.97,"body":"over sigma root two pi e to the"},{"speaker":"Patrick","startTime":1327.71,"endTime":1331.97,"body":"whatever, and you just drop in a"},{"speaker":"Patrick","startTime":1331.97,"endTime":1337.43,"body":"mean vector and a covariance"},{"speaker":"Patrick","startTime":1331.97,"endTime":1337.43,"body":"matrix and a vector of observed"},{"speaker":"Patrick","startTime":1337.43,"endTime":1340.13,"body":"values. And now it's a"},{"speaker":"Patrick","startTime":1337.43,"endTime":1340.13,"body":"multivariate normal"},{"speaker":"Patrick","startTime":1340.13,"endTime":1343.64,"body":"distribution, and everything"},{"speaker":"Patrick","startTime":1340.13,"endTime":1343.64,"body":"just scales up. And instead of"},{"speaker":"Patrick","startTime":1343.64,"endTime":1346.58,"body":"taking a derivative, you take"},{"speaker":"Patrick","startTime":1343.64,"endTime":1346.58,"body":"partial derivatives, you take"},{"speaker":"Patrick","startTime":1346.58,"endTime":1350.87,"body":"derivatives with respect to each"},{"speaker":"Patrick","startTime":1346.58,"endTime":1350.87,"body":"parameter, everything just"},{"speaker":"Patrick","startTime":1350.87,"endTime":1354.74,"body":"scales up. Here's where we can"},{"speaker":"Patrick","startTime":1350.87,"endTime":1354.74,"body":"do one little fix up. And this"},{"speaker":"Patrick","startTime":1354.74,"endTime":1360.2,"body":"is another very confusing thing"},{"speaker":"Patrick","startTime":1354.74,"endTime":1360.2,"body":"that you encounter. When we do"},{"speaker":"Patrick","startTime":1360.29,"endTime":1363.35,"body":"the independent multiplication"},{"speaker":"Patrick","startTime":1360.29,"endTime":1363.35,"body":"of the likelihoods that we've"},{"speaker":"Patrick","startTime":1363.35,"endTime":1367.34,"body":"been talking about, well, small"},{"speaker":"Patrick","startTime":1363.35,"endTime":1367.34,"body":"numbers get smaller when you"},{"speaker":"Patrick","startTime":1367.34,"endTime":1371.3,"body":"multiply them point one times"},{"speaker":"Patrick","startTime":1367.34,"endTime":1371.3,"body":"point one times point one times"},{"speaker":"Patrick","startTime":1371.3,"endTime":1376.31,"body":"point one starts getting really,"},{"speaker":"Patrick","startTime":1371.3,"endTime":1376.31,"body":"really small. I mean, it starts"},{"speaker":"Patrick","startTime":1376.31,"endTime":1379.73,"body":"getting small to the point where"},{"speaker":"Patrick","startTime":1376.31,"endTime":1379.73,"body":"your first significant digit can"},{"speaker":"Patrick","startTime":1379.73,"endTime":1382.61,"body":"be 810 12 decimal points out,"},{"speaker":"Greg","startTime":1382.76,"endTime":1384.53,"body":"oh, yeah, at least. So"},{"speaker":"Patrick","startTime":1384.56,"endTime":1389.78,"body":"we do a little judo"},{"speaker":"Patrick","startTime":1384.56,"endTime":1389.78,"body":"move one thing out of the way to"},{"speaker":"Patrick","startTime":1389.78,"endTime":1394.73,"body":"do something else with it. And I"},{"speaker":"Patrick","startTime":1389.78,"endTime":1394.73,"body":"say, I remember in ninth grade,"},{"speaker":"Patrick","startTime":1395.27,"endTime":1401.27,"body":"that logs are magical, we are"},{"speaker":"Patrick","startTime":1395.27,"endTime":1401.27,"body":"going to take the natural log of"},{"speaker":"Patrick","startTime":1401.27,"endTime":1405.92,"body":"that likelihood expression. And"},{"speaker":"Patrick","startTime":1401.27,"endTime":1405.92,"body":"what that does is when you have"},{"speaker":"Patrick","startTime":1405.92,"endTime":1411.59,"body":"an exponent in products, natural"},{"speaker":"Patrick","startTime":1405.92,"endTime":1411.59,"body":"logs magically change products"},{"speaker":"Patrick","startTime":1411.62,"endTime":1415.94,"body":"to sums. And so what we're going"},{"speaker":"Patrick","startTime":1411.62,"endTime":1415.94,"body":"to do is we're going to use this"},{"speaker":"Patrick","startTime":1415.94,"endTime":1419.78,"body":"natural log transformation,"},{"speaker":"Patrick","startTime":1415.94,"endTime":1419.78,"body":"which by the way, is monotonic,"},{"speaker":"Patrick","startTime":1420.02,"endTime":1423.38,"body":"meaning that the maximum value"},{"speaker":"Patrick","startTime":1420.02,"endTime":1423.38,"body":"of one is the same as the"},{"speaker":"Patrick","startTime":1423.38,"endTime":1426.47,"body":"maximum value of the other. But"},{"speaker":"Patrick","startTime":1423.38,"endTime":1426.47,"body":"that is where you're reading"},{"speaker":"Patrick","startTime":1426.47,"endTime":1429.35,"body":"your own work, or you're taught"},{"speaker":"Patrick","startTime":1426.47,"endTime":1429.35,"body":"in a class that we're trying to"},{"speaker":"Patrick","startTime":1429.35,"endTime":1432.89,"body":"maximize the log of the"},{"speaker":"Patrick","startTime":1429.35,"endTime":1432.89,"body":"likelihood. That's why we're"},{"speaker":"Patrick","startTime":1432.89,"endTime":1436.76,"body":"doing it's just a monotonic"},{"speaker":"Patrick","startTime":1432.89,"endTime":1436.76,"body":"transformation. And then one"},{"speaker":"Patrick","startTime":1436.76,"endTime":1442.22,"body":"last little thing we sometimes"},{"speaker":"Patrick","startTime":1436.76,"endTime":1442.22,"body":"do is in the normal expression,"},{"speaker":"Patrick","startTime":1442.22,"endTime":1445.55,"body":"that probability density"},{"speaker":"Patrick","startTime":1442.22,"endTime":1445.55,"body":"function in the cockpit of the"},{"speaker":"Patrick","startTime":1445.55,"endTime":1449.84,"body":"exponent is a negative one half."},{"speaker":"Patrick","startTime":1445.55,"endTime":1449.84,"body":"And it's just there, it's fine."},{"speaker":"Patrick","startTime":1449.84,"endTime":1452.69,"body":"It's just minding its own"},{"speaker":"Patrick","startTime":1449.84,"endTime":1452.69,"body":"business. But if we multiplied"},{"speaker":"Patrick","startTime":1452.69,"endTime":1456.08,"body":"by negative two, it just makes"},{"speaker":"Patrick","startTime":1452.69,"endTime":1456.08,"body":"it go way tidies house a little"},{"speaker":"Patrick","startTime":1456.08,"endTime":1460.79,"body":"bit. And so what we're ended up"},{"speaker":"Patrick","startTime":1456.08,"endTime":1460.79,"body":"with is negative two times the"},{"speaker":"Patrick","startTime":1460.79,"endTime":1465.29,"body":"log of the likelihood is what"},{"speaker":"Patrick","startTime":1460.79,"endTime":1465.29,"body":"we're trying to optimize when we"},{"speaker":"Patrick","startTime":1465.29,"endTime":1468.14,"body":"use maximum likelihood to get"},{"speaker":"Patrick","startTime":1465.29,"endTime":1468.14,"body":"these parameter estimates."},{"speaker":"Greg","startTime":1468.26,"endTime":1471.14,"body":"And that was sneaky how"},{"speaker":"Greg","startTime":1468.26,"endTime":1471.14,"body":"you use the word optimize it,"},{"speaker":"Greg","startTime":1471.14,"endTime":1477.32,"body":"you see, because I didn't"},{"speaker":"Greg","startTime":1471.14,"endTime":1477.32,"body":"notice. I did I did so. So just"},{"speaker":"Greg","startTime":1477.32,"endTime":1482.81,"body":"to be clear, when we try to"},{"speaker":"Greg","startTime":1477.32,"endTime":1482.81,"body":"maximize the likelihood that is"},{"speaker":"Greg","startTime":1482.81,"endTime":1487.79,"body":"the same as maximizing the log"},{"speaker":"Greg","startTime":1482.81,"endTime":1487.79,"body":"of the likelihood of all of the"},{"speaker":"Greg","startTime":1487.79,"endTime":1491.12,"body":"observations. So rather than"},{"speaker":"Greg","startTime":1487.79,"endTime":1491.12,"body":"maximizing the product, which is"},{"speaker":"Greg","startTime":1491.12,"endTime":1494.57,"body":"the likelihood we maximize the"},{"speaker":"Greg","startTime":1491.12,"endTime":1494.57,"body":"sum of the logs, which is the"},{"speaker":"Greg","startTime":1494.57,"endTime":1497.84,"body":"log likelihood, but when you"},{"speaker":"Greg","startTime":1494.57,"endTime":1497.84,"body":"multiply that by minus two it"},{"speaker":"Greg","startTime":1497.84,"endTime":1502.16,"body":"flips so we don't try to match"},{"speaker":"Greg","startTime":1497.84,"endTime":1502.16,"body":"maximize the negative two log"},{"speaker":"Greg","startTime":1502.16,"endTime":1505.16,"body":"likelihood we actually try to"},{"speaker":"Greg","startTime":1502.16,"endTime":1505.16,"body":"minimize the negative two log"},{"speaker":"Greg","startTime":1505.16,"endTime":1507.98,"body":"likelihood. So this becomes a"},{"speaker":"Greg","startTime":1505.16,"endTime":1507.98,"body":"problem of minimizing a"},{"speaker":"Greg","startTime":1507.98,"endTime":1510.2,"body":"particular function. And I will"},{"speaker":"Greg","startTime":1507.98,"endTime":1510.2,"body":"tell you, even though it's"},{"speaker":"Greg","startTime":1510.2,"endTime":1513.38,"body":"maximum likelihood, the idea of"},{"speaker":"Greg","startTime":1510.2,"endTime":1513.38,"body":"minimizing this function still"},{"speaker":"Greg","startTime":1513.38,"endTime":1515.78,"body":"feels good because we're trying"},{"speaker":"Greg","startTime":1513.38,"endTime":1515.78,"body":"to minimize the amount of"},{"speaker":"Greg","startTime":1515.78,"endTime":1518.57,"body":"badness of fit. So I'm totally"},{"speaker":"Greg","startTime":1515.78,"endTime":1518.57,"body":"cool with the minus two log"},{"speaker":"Greg","startTime":1518.57,"endTime":1519.02,"body":"likelihood"},{"speaker":"Patrick","startTime":1519.05,"endTime":1521.18,"body":"I am, but this is why"},{"speaker":"Patrick","startTime":1519.05,"endTime":1521.18,"body":"people hate us."},{"speaker":"Greg","startTime":1522.56,"endTime":1526.61,"body":"That's it. That's the"},{"speaker":"Greg","startTime":1522.56,"endTime":1526.61,"body":"reason why the minus two,"},{"speaker":"Patrick","startTime":1526.61,"endTime":1531.11,"body":"let me see, let me pull"},{"speaker":"Patrick","startTime":1526.61,"endTime":1531.11,"body":"down the third volume, part C,"},{"speaker":"Patrick","startTime":1532.13,"endTime":1537.56,"body":"section A, of why people hate"},{"speaker":"Patrick","startTime":1532.13,"endTime":1537.56,"body":"us. You're trying to minimize"},{"speaker":"Patrick","startTime":1537.56,"endTime":1542.09,"body":"the Fit function to get the"},{"speaker":"Patrick","startTime":1537.56,"endTime":1542.09,"body":"maximum likelihood estimate."},{"speaker":"Patrick","startTime":1542.18,"endTime":1546.08,"body":"Yeah. Or it's not why people"},{"speaker":"Patrick","startTime":1542.18,"endTime":1546.08,"body":"hate us, but it's certainly on"},{"speaker":"Patrick","startTime":1546.08,"endTime":1550.01,"body":"the list. But as Greg just"},{"speaker":"Patrick","startTime":1546.08,"endTime":1550.01,"body":"really nicely described, these"},{"speaker":"Patrick","startTime":1550.01,"endTime":1552.62,"body":"are all monotonic"},{"speaker":"Patrick","startTime":1550.01,"endTime":1552.62,"body":"transformations. And so the"},{"speaker":"Patrick","startTime":1552.62,"endTime":1555.56,"body":"value that maximizes the"},{"speaker":"Patrick","startTime":1552.62,"endTime":1555.56,"body":"likelihood is the same as the"},{"speaker":"Patrick","startTime":1555.56,"endTime":1559.04,"body":"value that maximizes the log of"},{"speaker":"Patrick","startTime":1555.56,"endTime":1559.04,"body":"the likelihood is the same as"},{"speaker":"Patrick","startTime":1559.04,"endTime":1562.82,"body":"the value that minimizes"},{"speaker":"Patrick","startTime":1559.04,"endTime":1562.82,"body":"negative two times the log of"},{"speaker":"Patrick","startTime":1562.82,"endTime":1566.42,"body":"the likelihood. So they're all"},{"speaker":"Patrick","startTime":1562.82,"endTime":1566.42,"body":"the same things. We're just"},{"speaker":"Patrick","startTime":1566.42,"endTime":1569.27,"body":"using these things to our"},{"speaker":"Patrick","startTime":1566.42,"endTime":1569.27,"body":"advantage, right? It makes it"},{"speaker":"Patrick","startTime":1569.3,"endTime":1572.45,"body":"easier, it makes it more"},{"speaker":"Patrick","startTime":1569.3,"endTime":1572.45,"body":"tractable. If you're a multi"},{"speaker":"Patrick","startTime":1572.45,"endTime":1576.47,"body":"level modeler and you've heard"},{"speaker":"Patrick","startTime":1572.45,"endTime":1576.47,"body":"the term deviance, well,"},{"speaker":"Patrick","startTime":1576.47,"endTime":1579.83,"body":"deviance is negative two times"},{"speaker":"Patrick","startTime":1576.47,"endTime":1579.83,"body":"the log likelihood."},{"speaker":"Greg","startTime":1579.86,"endTime":1581.69,"body":"So is that what that"},{"speaker":"Greg","startTime":1579.86,"endTime":1581.69,"body":"person meant when they said we"},{"speaker":"Greg","startTime":1581.69,"endTime":1585.41,"body":"are deviance? That's what I'm"},{"speaker":"Greg","startTime":1581.69,"endTime":1585.41,"body":"going to go with? Okay. Well,"},{"speaker":"Greg","startTime":1585.41,"endTime":1587.21,"body":"that makes sense when"},{"speaker":"Patrick","startTime":1587.21,"endTime":1588.77,"body":"that person was my"},{"speaker":"Patrick","startTime":1587.21,"endTime":1588.77,"body":"daughter."},{"speaker":"Greg","startTime":1591.05,"endTime":1594.02,"body":"Alright, so before we move"},{"speaker":"Greg","startTime":1591.05,"endTime":1594.02,"body":"on, I want to give one attempt"},{"speaker":"Greg","startTime":1594.02,"endTime":1596.57,"body":"at visualizing what's going on."},{"speaker":"Greg","startTime":1594.02,"endTime":1596.57,"body":"And that is something I've"},{"speaker":"Greg","startTime":1596.57,"endTime":1599.96,"body":"mentioned before, which, which"},{"speaker":"Greg","startTime":1596.57,"endTime":1599.96,"body":"is the circus tent. Let's"},{"speaker":"Greg","startTime":1599.96,"endTime":1603.11,"body":"imagine just temporarily that we"},{"speaker":"Greg","startTime":1599.96,"endTime":1603.11,"body":"are doing the smallest"},{"speaker":"Greg","startTime":1603.11,"endTime":1606.47,"body":"multivariate example where we"},{"speaker":"Greg","startTime":1603.11,"endTime":1606.47,"body":"have two variables. And this"},{"speaker":"Greg","startTime":1606.47,"endTime":1609.41,"body":"extends to many variables, but"},{"speaker":"Greg","startTime":1606.47,"endTime":1609.41,"body":"we got two variables x one and x"},{"speaker":"Greg","startTime":1609.41,"endTime":1614.06,"body":"two, so that people can be"},{"speaker":"Greg","startTime":1609.41,"endTime":1614.06,"body":"thought of as standing on a"},{"speaker":"Greg","startTime":1614.06,"endTime":1619.13,"body":"plane on a grid. So if my score"},{"speaker":"Greg","startTime":1614.06,"endTime":1619.13,"body":"on x one is four, and on x two"},{"speaker":"Greg","startTime":1619.13,"endTime":1624.74,"body":"is 13, then I go stand at 413."},{"speaker":"Greg","startTime":1619.13,"endTime":1624.74,"body":"We have everybody go stand on"},{"speaker":"Greg","startTime":1624.74,"endTime":1627.92,"body":"the floor at the location that"},{"speaker":"Greg","startTime":1624.74,"endTime":1627.92,"body":"corresponds to their x one and"},{"speaker":"Greg","startTime":1627.92,"endTime":1632.51,"body":"their x two points. And now what"},{"speaker":"Greg","startTime":1627.92,"endTime":1632.51,"body":"we have to do is put a tent"},{"speaker":"Greg","startTime":1632.54,"endTime":1637.88,"body":"overhead. But the criterion is"},{"speaker":"Greg","startTime":1632.54,"endTime":1637.88,"body":"that the tent is as high above"},{"speaker":"Greg","startTime":1637.91,"endTime":1642.17,"body":"people's heads as possible."},{"speaker":"Greg","startTime":1637.91,"endTime":1642.17,"body":"Collectively. That means that if"},{"speaker":"Greg","startTime":1642.17,"endTime":1645.29,"body":"we are all standing toward the"},{"speaker":"Greg","startTime":1642.17,"endTime":1645.29,"body":"middle, we're not going to put"},{"speaker":"Greg","startTime":1645.29,"endTime":1648.44,"body":"the tent three kilometers down"},{"speaker":"Greg","startTime":1645.29,"endTime":1648.44,"body":"to the left, we want to have"},{"speaker":"Greg","startTime":1648.44,"endTime":1651.59,"body":"some tent that is overhead and"},{"speaker":"Greg","startTime":1648.44,"endTime":1651.59,"body":"the things that we're allowed to"},{"speaker":"Greg","startTime":1651.59,"endTime":1655.73,"body":"move. Well, if we decided to"},{"speaker":"Greg","startTime":1651.59,"endTime":1655.73,"body":"normal tent, a normal theory"},{"speaker":"Greg","startTime":1655.73,"endTime":1658.13,"body":"tent, we're just throwing that"},{"speaker":"Greg","startTime":1655.73,"endTime":1658.13,"body":"around as though Oh, it's a"},{"speaker":"Greg","startTime":1658.13,"endTime":1660.71,"body":"given that it's normal. But"},{"speaker":"Greg","startTime":1658.13,"endTime":1660.71,"body":"that's an assumption, right? If"},{"speaker":"Greg","startTime":1660.71,"endTime":1664.34,"body":"it is a multivariate normal"},{"speaker":"Greg","startTime":1660.71,"endTime":1664.34,"body":"tent, then what we have to do is"},{"speaker":"Greg","startTime":1664.34,"endTime":1668.21,"body":"decide where are we going to"},{"speaker":"Greg","startTime":1664.34,"endTime":1668.21,"body":"center this tent? And then how"},{"speaker":"Greg","startTime":1668.21,"endTime":1671.72,"body":"stretched out are we going to"},{"speaker":"Greg","startTime":1668.21,"endTime":1671.72,"body":"make that tent how stretched out"},{"speaker":"Greg","startTime":1671.72,"endTime":1674.48,"body":"in the x one direction, how"},{"speaker":"Greg","startTime":1671.72,"endTime":1674.48,"body":"stretched out in the x two"},{"speaker":"Greg","startTime":1674.48,"endTime":1678.11,"body":"direction, and then how much"},{"speaker":"Greg","startTime":1674.48,"endTime":1678.11,"body":"we're allowing the tent to"},{"speaker":"Greg","startTime":1678.11,"endTime":1681.98,"body":"reflect how much x one and x two"},{"speaker":"Greg","startTime":1678.11,"endTime":1681.98,"body":"might be related to each other."},{"speaker":"Greg","startTime":1682.25,"endTime":1686.87,"body":"And rage Hawk is going to her"},{"speaker":"Greg","startTime":1682.25,"endTime":1686.87,"body":"moving the tent, squishing the"},{"speaker":"Greg","startTime":1686.87,"endTime":1690.8,"body":"tent, doing all of that kind of"},{"speaker":"Greg","startTime":1686.87,"endTime":1690.8,"body":"stuff. In the end, everybody has"},{"speaker":"Greg","startTime":1690.8,"endTime":1694.37,"body":"a tent above their head to a"},{"speaker":"Greg","startTime":1690.8,"endTime":1694.37,"body":"certain height. And if a lot of"},{"speaker":"Greg","startTime":1694.37,"endTime":1697.37,"body":"people have the tent nicely high"},{"speaker":"Greg","startTime":1694.37,"endTime":1697.37,"body":"above their heads, they are very"},{"speaker":"Greg","startTime":1697.37,"endTime":1700.73,"body":"likely in that multivariate"},{"speaker":"Greg","startTime":1697.37,"endTime":1700.73,"body":"space. And if the tent is"},{"speaker":"Greg","startTime":1700.73,"endTime":1703.46,"body":"crashing down on top of their"},{"speaker":"Greg","startTime":1700.73,"endTime":1703.46,"body":"head, then they have a very"},{"speaker":"Greg","startTime":1703.46,"endTime":1707.18,"body":"small likelihood in that"},{"speaker":"Greg","startTime":1703.46,"endTime":1707.18,"body":"multivariate space. And what do"},{"speaker":"Greg","startTime":1707.18,"endTime":1710.12,"body":"we do exactly what Patrick said"},{"speaker":"Greg","startTime":1707.18,"endTime":1710.12,"body":"we take everyone's likelihood,"},{"speaker":"Greg","startTime":1710.24,"endTime":1713.96,"body":"we multiply them, we take the"},{"speaker":"Greg","startTime":1710.24,"endTime":1713.96,"body":"logarithm, we multiply it by"},{"speaker":"Greg","startTime":1713.96,"endTime":1717.41,"body":"negative two to try to decide"},{"speaker":"Greg","startTime":1713.96,"endTime":1717.41,"body":"what is the negative two log"},{"speaker":"Greg","startTime":1717.41,"endTime":1721.43,"body":"likelihood associated with those"},{"speaker":"Greg","startTime":1717.41,"endTime":1721.43,"body":"data. Given that location of the"},{"speaker":"Greg","startTime":1721.43,"endTime":1724.58,"body":"tent rage Hulk moves the tent"},{"speaker":"Greg","startTime":1721.43,"endTime":1724.58,"body":"all over the place repeating"},{"speaker":"Greg","startTime":1724.58,"endTime":1727.88,"body":"this process over and over and"},{"speaker":"Greg","startTime":1724.58,"endTime":1727.88,"body":"over in two dimensional space."},{"speaker":"Greg","startTime":1728.3,"endTime":1732.08,"body":"But hot Hulk sexy Hulk can"},{"speaker":"Greg","startTime":1728.3,"endTime":1732.08,"body":"derive exactly where that tent"},{"speaker":"Greg","startTime":1732.08,"endTime":1735.02,"body":"needs to be centered how"},{"speaker":"Greg","startTime":1732.08,"endTime":1735.02,"body":"stretched it needs to be in the"},{"speaker":"Greg","startTime":1735.02,"endTime":1737.96,"body":"x one direction, that's the"},{"speaker":"Greg","startTime":1735.02,"endTime":1737.96,"body":"variance how stretched it needs"},{"speaker":"Greg","startTime":1737.96,"endTime":1741.38,"body":"to be in the x two direction."},{"speaker":"Greg","startTime":1737.96,"endTime":1741.38,"body":"That's the variance and how much"},{"speaker":"Greg","startTime":1741.38,"endTime":1745.1,"body":"those two relate to each other."},{"speaker":"Greg","startTime":1741.38,"endTime":1745.1,"body":"That's the covariance. And all"},{"speaker":"Greg","startTime":1745.1,"endTime":1747.02,"body":"of that is done by calculus."},{"speaker":"Patrick","startTime":1747.08,"endTime":1753.14,"body":"But we still need rage,"},{"speaker":"Patrick","startTime":1747.08,"endTime":1753.14,"body":"HK. This is a value it is always"},{"speaker":"Patrick","startTime":1753.14,"endTime":1759.41,"body":"about me. In Episode 102, this"},{"speaker":"Patrick","startTime":1753.14,"endTime":1759.41,"body":"is just dawning on you this just"},{"speaker":"Patrick","startTime":1759.41,"endTime":1764.27,"body":"in it's all about Patrick sexy"},{"speaker":"Patrick","startTime":1759.41,"endTime":1764.27,"body":"Hulk can do those normal"},{"speaker":"Patrick","startTime":1764.27,"endTime":1767.51,"body":"equations, where you lay out the"},{"speaker":"Patrick","startTime":1764.27,"endTime":1767.51,"body":"derivatives, you set them to"},{"speaker":"Patrick","startTime":1767.51,"endTime":1772.76,"body":"zero and you solve up to a"},{"speaker":"Patrick","startTime":1767.51,"endTime":1772.76,"body":"point. And then you can no"},{"speaker":"Patrick","startTime":1772.76,"endTime":1777.26,"body":"longer for complicated models."},{"speaker":"Patrick","startTime":1772.76,"endTime":1777.26,"body":"You can't calculate these"},{"speaker":"Patrick","startTime":1777.26,"endTime":1779.42,"body":"derivatives in closed form"},{"speaker":"Patrick","startTime":1777.26,"endTime":1779.42,"body":"anymore."},{"speaker":"Greg","startTime":1779.45,"endTime":1781.52,"body":"You're absolutely right. I"},{"speaker":"Greg","startTime":1779.45,"endTime":1781.52,"body":"mean to a point you can do some"},{"speaker":"Greg","startTime":1781.52,"endTime":1785.33,"body":"of the mathematics because there"},{"speaker":"Greg","startTime":1781.52,"endTime":1785.33,"body":"is a whole matrix calculus where"},{"speaker":"Greg","startTime":1785.33,"endTime":1788.63,"body":"you can take derivatives with"},{"speaker":"Greg","startTime":1785.33,"endTime":1788.63,"body":"respect to vectors and matrices,"},{"speaker":"Greg","startTime":1788.63,"endTime":1791.57,"body":"and it does extend over. But as"},{"speaker":"Greg","startTime":1788.63,"endTime":1791.57,"body":"our models get more and more"},{"speaker":"Greg","startTime":1791.57,"endTime":1793.64,"body":"complicated, you're absolutely"},{"speaker":"Greg","startTime":1791.57,"endTime":1793.64,"body":"right. It just gets really"},{"speaker":"Greg","startTime":1793.64,"endTime":1798.56,"body":"really unwieldy even for sexy"},{"speaker":"Greg","startTime":1793.64,"endTime":1798.56,"body":"Hulk. And so what we can do is"},{"speaker":"Greg","startTime":1798.59,"endTime":1802.37,"body":"sort of feel our way over Round,"},{"speaker":"Greg","startTime":1798.59,"endTime":1802.37,"body":"let me give you an analogy. And"},{"speaker":"Greg","startTime":1802.37,"endTime":1805.19,"body":"I'm going to do it in terms of"},{"speaker":"Greg","startTime":1802.37,"endTime":1805.19,"body":"minimizing rather than"},{"speaker":"Greg","startTime":1805.19,"endTime":1808.28,"body":"maximizing, since we've earned"},{"speaker":"Greg","startTime":1805.19,"endTime":1808.28,"body":"our minus to log likelihood"},{"speaker":"Greg","startTime":1808.28,"endTime":1813.08,"body":"merit badge. Imagine that you"},{"speaker":"Greg","startTime":1808.28,"endTime":1813.08,"body":"parachuted into a valley at"},{"speaker":"Greg","startTime":1813.08,"endTime":1817.37,"body":"night, you can't see anything."},{"speaker":"Greg","startTime":1813.08,"endTime":1817.37,"body":"But your job is to find the"},{"speaker":"Greg","startTime":1817.37,"endTime":1820.55,"body":"lowest point in that valley. But"},{"speaker":"Greg","startTime":1817.37,"endTime":1820.55,"body":"it's pitch black, you can't see"},{"speaker":"Greg","startTime":1820.55,"endTime":1823.7,"body":"anything. And so what do you do"},{"speaker":"Greg","startTime":1820.55,"endTime":1823.7,"body":"you, wherever you land, you take"},{"speaker":"Greg","startTime":1823.7,"endTime":1826.67,"body":"a step in all the directions"},{"speaker":"Greg","startTime":1823.7,"endTime":1826.67,"body":"around you, and you go, ooh,"},{"speaker":"Greg","startTime":1826.67,"endTime":1829.52,"body":"that's downhill. So then you"},{"speaker":"Greg","startTime":1826.67,"endTime":1829.52,"body":"move in that direction, and then"},{"speaker":"Greg","startTime":1829.52,"endTime":1831.8,"body":"you take a step all around, you"},{"speaker":"Greg","startTime":1829.52,"endTime":1831.8,"body":"go, ooh, and that's more"},{"speaker":"Greg","startTime":1831.8,"endTime":1835.88,"body":"downhill. And you keep going,"},{"speaker":"Greg","startTime":1831.8,"endTime":1835.88,"body":"taking incremental steps over"},{"speaker":"Greg","startTime":1835.88,"endTime":1839.51,"body":"and over and over until you"},{"speaker":"Greg","startTime":1835.88,"endTime":1839.51,"body":"believe that you have found that"},{"speaker":"Greg","startTime":1839.54,"endTime":1843.68,"body":"lowest point. And"},{"speaker":"Greg","startTime":1839.54,"endTime":1843.68,"body":"mathematically, we can set up"},{"speaker":"Greg","startTime":1843.68,"endTime":1847.4,"body":"computer algorithms that do a"},{"speaker":"Greg","startTime":1843.68,"endTime":1847.4,"body":"much smarter version of that,"},{"speaker":"Greg","startTime":1847.46,"endTime":1850.4,"body":"where they move their foot"},{"speaker":"Greg","startTime":1847.46,"endTime":1850.4,"body":"around a particular point that"},{"speaker":"Greg","startTime":1850.4,"endTime":1854.27,"body":"corresponds to starting values."},{"speaker":"Greg","startTime":1850.4,"endTime":1854.27,"body":"And it doesn't just say, hey,"},{"speaker":"Greg","startTime":1854.27,"endTime":1857.36,"body":"things are going downhill that"},{"speaker":"Greg","startTime":1854.27,"endTime":1857.36,"body":"way, it says things like, it"},{"speaker":"Greg","startTime":1857.36,"endTime":1860.9,"body":"looks like it's really steep in"},{"speaker":"Greg","startTime":1857.36,"endTime":1860.9,"body":"that direction. So I'm not just"},{"speaker":"Greg","startTime":1860.9,"endTime":1862.79,"body":"going to take a little step in"},{"speaker":"Greg","startTime":1860.9,"endTime":1862.79,"body":"that direction, I'm going to"},{"speaker":"Greg","startTime":1862.79,"endTime":1868.22,"body":"take a big old step in that"},{"speaker":"Greg","startTime":1862.79,"endTime":1868.22,"body":"direction. So we have these"},{"speaker":"Greg","startTime":1868.22,"endTime":1871.61,"body":"different algorithms that sort"},{"speaker":"Greg","startTime":1868.22,"endTime":1871.61,"body":"of predict how far down it can"},{"speaker":"Greg","startTime":1871.61,"endTime":1874.79,"body":"go take a big leap in that"},{"speaker":"Greg","startTime":1871.61,"endTime":1874.79,"body":"particular direction, until it"},{"speaker":"Greg","startTime":1874.79,"endTime":1877.46,"body":"finds itself in a place where it"},{"speaker":"Greg","startTime":1874.79,"endTime":1877.46,"body":"sticks its toe all the way"},{"speaker":"Greg","startTime":1877.46,"endTime":1880.79,"body":"around and says everything gets"},{"speaker":"Greg","startTime":1877.46,"endTime":1880.79,"body":"higher around me. So"},{"speaker":"Greg","startTime":1880.79,"endTime":1884.9,"body":"congratulations, I must have"},{"speaker":"Greg","startTime":1880.79,"endTime":1884.9,"body":"reached that particular optimum,"},{"speaker":"Patrick","startTime":1885.11,"endTime":1886.19,"body":"unless you didn't."},{"speaker":"Greg","startTime":1887.21,"endTime":1891.68,"body":"Other than that. Yeah, so"},{"speaker":"Greg","startTime":1887.21,"endTime":1891.68,"body":"with a particularly messy"},{"speaker":"Greg","startTime":1891.68,"endTime":1895.97,"body":"likelihood terrain, you might be"},{"speaker":"Greg","startTime":1891.68,"endTime":1895.97,"body":"very, very proudly sitting in"},{"speaker":"Greg","startTime":1895.97,"endTime":1899.21,"body":"this place, that's actually kind"},{"speaker":"Greg","startTime":1895.97,"endTime":1899.21,"body":"of near the top, I just found"},{"speaker":"Greg","startTime":1899.21,"endTime":1902.78,"body":"this tiny little lake up here,"},{"speaker":"Greg","startTime":1899.21,"endTime":1902.78,"body":"Oh, isn't this nice, when the"},{"speaker":"Greg","startTime":1902.78,"endTime":1908.24,"body":"minimum, the global minimum of"},{"speaker":"Greg","startTime":1902.78,"endTime":1908.24,"body":"this function is way the heck"},{"speaker":"Greg","startTime":1908.24,"endTime":1911.3,"body":"and down there. And with more"},{"speaker":"Greg","startTime":1908.24,"endTime":1911.3,"body":"and more complicated models, you"},{"speaker":"Greg","startTime":1911.3,"endTime":1913.64,"body":"have to be very careful about"},{"speaker":"Greg","startTime":1911.3,"endTime":1913.64,"body":"this problem. And what that"},{"speaker":"Greg","startTime":1913.64,"endTime":1917.96,"body":"means is ideally, parachuting"},{"speaker":"Greg","startTime":1913.64,"endTime":1917.96,"body":"into this valley and landing in"},{"speaker":"Greg","startTime":1917.96,"endTime":1921.08,"body":"a whole bunch of different"},{"speaker":"Greg","startTime":1917.96,"endTime":1921.08,"body":"places, and seeing which one of"},{"speaker":"Greg","startTime":1921.08,"endTime":1923.9,"body":"those ultimately takes you to"},{"speaker":"Greg","startTime":1921.08,"endTime":1923.9,"body":"the lowest point possible."},{"speaker":"Patrick","startTime":1924.11,"endTime":1926.96,"body":"And if you flip it the"},{"speaker":"Patrick","startTime":1924.11,"endTime":1926.96,"body":"other way, if any of you are"},{"speaker":"Patrick","startTime":1926.96,"endTime":1930.05,"body":"hikers or mountain climbers, I'm"},{"speaker":"Patrick","startTime":1926.96,"endTime":1930.05,"body":"not a mountain climber, but I"},{"speaker":"Patrick","startTime":1930.05,"endTime":1933.8,"body":"really liked hiking and did a"},{"speaker":"Patrick","startTime":1930.05,"endTime":1933.8,"body":"lot of that in Colorado. And"},{"speaker":"Patrick","startTime":1933.8,"endTime":1937.58,"body":"there's a thing called a false"},{"speaker":"Patrick","startTime":1933.8,"endTime":1937.58,"body":"Summit. And you're climbing up"},{"speaker":"Patrick","startTime":1937.61,"endTime":1942.68,"body":"and you see the top, and you get"},{"speaker":"Patrick","startTime":1937.61,"endTime":1942.68,"body":"in your head that you're near"},{"speaker":"Patrick","startTime":1942.68,"endTime":1946.43,"body":"the top, and you come out"},{"speaker":"Patrick","startTime":1942.68,"endTime":1946.43,"body":"through the trees, and then the"},{"speaker":"Patrick","startTime":1946.46,"endTime":1948.89,"body":"actual mountain is behind that,"},{"speaker":"Greg","startTime":1949.459,"endTime":1950.899,"body":"just as you're about to"},{"speaker":"Greg","startTime":1949.459,"endTime":1950.899,"body":"yodel."},{"speaker":"Patrick","startTime":1954.41,"endTime":1958.07,"body":"So flipping that around"},{"speaker":"Patrick","startTime":1954.41,"endTime":1958.07,"body":"to the minimizing, as you said,"},{"speaker":"Patrick","startTime":1958.07,"endTime":1961.58,"body":"of getting into the little lake"},{"speaker":"Patrick","startTime":1958.07,"endTime":1961.58,"body":"near the top is we call that a"},{"speaker":"Patrick","startTime":1961.58,"endTime":1964.64,"body":"local minima as opposed to the"},{"speaker":"Patrick","startTime":1961.58,"endTime":1964.64,"body":"global minima. And there are"},{"speaker":"Patrick","startTime":1964.64,"endTime":1968.75,"body":"ways that we can protect against"},{"speaker":"Patrick","startTime":1964.64,"endTime":1968.75,"body":"that. Fortunately, for a lot of"},{"speaker":"Patrick","startTime":1968.75,"endTime":1973.73,"body":"models, that is not common. It"},{"speaker":"Patrick","startTime":1968.75,"endTime":1973.73,"body":"is in other more complicated"},{"speaker":"Patrick","startTime":1973.73,"endTime":1976.97,"body":"things, this is actually a real"},{"speaker":"Patrick","startTime":1973.73,"endTime":1976.97,"body":"problem and mixture modeling."},{"speaker":"Patrick","startTime":1977.63,"endTime":1981.74,"body":"That's where randomize start"},{"speaker":"Patrick","startTime":1977.63,"endTime":1981.74,"body":"values come from, and you do one"},{"speaker":"Patrick","startTime":1981.74,"endTime":1986.48,"body":"or 2000 Different start values."},{"speaker":"Patrick","startTime":1981.74,"endTime":1986.48,"body":"So there are lots of ways we can"},{"speaker":"Patrick","startTime":1986.48,"endTime":1991.4,"body":"deal with that. What we"},{"speaker":"Patrick","startTime":1986.48,"endTime":1991.4,"body":"sometimes find is not so much a"},{"speaker":"Patrick","startTime":1991.4,"endTime":1995.15,"body":"local minima, but at least in"},{"speaker":"Patrick","startTime":1991.4,"endTime":1995.15,"body":"some of my work is it's what's"},{"speaker":"Patrick","startTime":1995.15,"endTime":1998.69,"body":"called a flat spot. And that's"},{"speaker":"Patrick","startTime":1995.15,"endTime":1998.69,"body":"where you get out on the"},{"speaker":"Patrick","startTime":1998.69,"endTime":2001.87,"body":"likelihood. And there's just not"},{"speaker":"Patrick","startTime":1998.69,"endTime":2001.87,"body":"a lot of change in any"},{"speaker":"Patrick","startTime":2001.87,"endTime":2004.75,"body":"direction. And so you kind of"},{"speaker":"Patrick","startTime":2001.87,"endTime":2004.75,"body":"look over here, and then you go"},{"speaker":"Patrick","startTime":2004.75,"endTime":2006.64,"body":"over here, and then you go over"},{"speaker":"Patrick","startTime":2004.75,"endTime":2006.64,"body":"here, and then you go back. And"},{"speaker":"Patrick","startTime":2006.64,"endTime":2009.58,"body":"you're kind of back to where you"},{"speaker":"Patrick","startTime":2006.64,"endTime":2009.58,"body":"were before, if you've heard the"},{"speaker":"Patrick","startTime":2009.58,"endTime":2012.82,"body":"term is sometimes called a flat"},{"speaker":"Patrick","startTime":2009.58,"endTime":2012.82,"body":"spot, very"},{"speaker":"Greg","startTime":2012.82,"endTime":2016.9,"body":"technical term. In the"},{"speaker":"Greg","startTime":2012.82,"endTime":2016.9,"body":"sciences, we call that a flat"},{"speaker":"Greg","startTime":2016.9,"endTime":2017.41,"body":"flat spot."},{"speaker":"Patrick","startTime":2017.5,"endTime":2022.48,"body":"Exactly. So these are"},{"speaker":"Patrick","startTime":2017.5,"endTime":2022.48,"body":"all different ways of saying how"},{"speaker":"Patrick","startTime":2022.48,"endTime":2026.89,"body":"do we obtain a set of sample"},{"speaker":"Patrick","startTime":2022.48,"endTime":2026.89,"body":"estimates of unknown population"},{"speaker":"Patrick","startTime":2026.89,"endTime":2032.2,"body":"parameters that maximizes the"},{"speaker":"Patrick","startTime":2026.89,"endTime":2032.2,"body":"joint likelihood of our sample"},{"speaker":"Patrick","startTime":2032.2,"endTime":2037.27,"body":"data. That's what Fisher gave us"},{"speaker":"Patrick","startTime":2032.2,"endTime":2037.27,"body":"in the field. Now, I will toss"},{"speaker":"Patrick","startTime":2037.27,"endTime":2042.16,"body":"it back to you to say, Okay, we"},{"speaker":"Patrick","startTime":2037.27,"endTime":2042.16,"body":"get a point estimate, well done"},{"speaker":"Patrick","startTime":2042.16,"endTime":2047.41,"body":"you. But we need some kind of"},{"speaker":"Patrick","startTime":2042.16,"endTime":2047.41,"body":"estimate of the variability of"},{"speaker":"Patrick","startTime":2047.41,"endTime":2051.16,"body":"that picture to simple"},{"speaker":"Patrick","startTime":2047.41,"endTime":2051.16,"body":"likelihoods around a parameter."},{"speaker":"Patrick","startTime":2051.25,"endTime":2054.07,"body":"Think of the egg that we talked"},{"speaker":"Patrick","startTime":2051.25,"endTime":2054.07,"body":"about in the ordinary least"},{"speaker":"Patrick","startTime":2054.07,"endTime":2058.09,"body":"squares, you can chart out a"},{"speaker":"Patrick","startTime":2054.07,"endTime":2058.09,"body":"parabola. And the bottom of that"},{"speaker":"Patrick","startTime":2058.09,"endTime":2061.66,"body":"parabola is the best possible"},{"speaker":"Patrick","startTime":2058.09,"endTime":2061.66,"body":"fit picture two parabolas that"},{"speaker":"Patrick","startTime":2061.66,"endTime":2066.16,"body":"have the same bottom, but one is"},{"speaker":"Patrick","startTime":2061.66,"endTime":2066.16,"body":"a really steep parabola. And one"},{"speaker":"Patrick","startTime":2066.16,"endTime":2072.1,"body":"is kind of a flat or parabola."},{"speaker":"Patrick","startTime":2066.16,"endTime":2072.1,"body":"It's just not as self confident."},{"speaker":"Patrick","startTime":2072.64,"endTime":2076.84,"body":"Walk us through the personality"},{"speaker":"Patrick","startTime":2072.64,"endTime":2076.84,"body":"differences of those two"},{"speaker":"Patrick","startTime":2076.84,"endTime":2082.69,"body":"parabolas. And how we can get an"},{"speaker":"Patrick","startTime":2076.84,"endTime":2082.69,"body":"estimate of the variability of"},{"speaker":"Patrick","startTime":2082.69,"endTime":2085.42,"body":"that maximum likelihood point"},{"speaker":"Patrick","startTime":2082.69,"endTime":2085.42,"body":"that we derived"},{"speaker":"Greg","startTime":2085.45,"endTime":2089.62,"body":"if we have found our way"},{"speaker":"Greg","startTime":2085.45,"endTime":2089.62,"body":"to whether we're talking about"},{"speaker":"Greg","startTime":2089.62,"endTime":2093.16,"body":"the top of the mountain No, no,"},{"speaker":"Greg","startTime":2089.62,"endTime":2093.16,"body":"right, right, fine, whatever."},{"speaker":"Greg","startTime":2093.28,"endTime":2095.65,"body":"I'm gonna continue with my"},{"speaker":"Greg","startTime":2093.28,"endTime":2095.65,"body":"valley thinking about this as"},{"speaker":"Greg","startTime":2095.65,"endTime":2098.41,"body":"minimizing something right. If"},{"speaker":"Greg","startTime":2095.65,"endTime":2098.41,"body":"we think about it from an"},{"speaker":"Greg","startTime":2098.41,"endTime":2102.79,"body":"analytical standpoint, so sexi"},{"speaker":"Greg","startTime":2098.41,"endTime":2102.79,"body":"Hawk who finds out by setting"},{"speaker":"Greg","startTime":2102.79,"endTime":2106.57,"body":"where the derivative is zero,"},{"speaker":"Greg","startTime":2102.79,"endTime":2106.57,"body":"what that means is that the"},{"speaker":"Greg","startTime":2106.57,"endTime":2110.11,"body":"tangent to the curve of the"},{"speaker":"Greg","startTime":2106.57,"endTime":2110.11,"body":"function is flat, it has no"},{"speaker":"Greg","startTime":2110.11,"endTime":2113.08,"body":"slope. So that's how we find"},{"speaker":"Greg","startTime":2110.11,"endTime":2113.08,"body":"where the minimum is, you know,"},{"speaker":"Greg","startTime":2113.08,"endTime":2116.23,"body":"especially for a function that's"},{"speaker":"Greg","startTime":2113.08,"endTime":2116.23,"body":"easy to navigate. But just like"},{"speaker":"Greg","startTime":2116.23,"endTime":2119.74,"body":"Patrick said, it might be the"},{"speaker":"Greg","startTime":2116.23,"endTime":2119.74,"body":"case that the parabola just kind"},{"speaker":"Greg","startTime":2119.74,"endTime":2124.39,"body":"of lazily on confidently wanders"},{"speaker":"Greg","startTime":2119.74,"endTime":2124.39,"body":"away from that low point, as"},{"speaker":"Greg","startTime":2124.39,"endTime":2127.84,"body":"opposed to another parabola that"},{"speaker":"Greg","startTime":2124.39,"endTime":2127.84,"body":"is just super sure of itself."},{"speaker":"Greg","startTime":2128.2,"endTime":2132.85,"body":"What that means is that that"},{"speaker":"Greg","startTime":2128.2,"endTime":2132.85,"body":"line, that slope that sits at"},{"speaker":"Greg","startTime":2132.85,"endTime":2138.52,"body":"the bottom that is perfectly"},{"speaker":"Greg","startTime":2132.85,"endTime":2138.52,"body":"flat, if in the lazy parabola,"},{"speaker":"Greg","startTime":2138.67,"endTime":2142.51,"body":"we move it a little bit away,"},{"speaker":"Greg","startTime":2138.67,"endTime":2142.51,"body":"the slope just changes a tiny"},{"speaker":"Greg","startTime":2142.51,"endTime":2146.05,"body":"bit, it just kind of goes up"},{"speaker":"Greg","startTime":2142.51,"endTime":2146.05,"body":"ever so slightly, in the"},{"speaker":"Greg","startTime":2146.05,"endTime":2149.56,"body":"confident parabola, that really"},{"speaker":"Greg","startTime":2146.05,"endTime":2149.56,"body":"tight parabola around the"},{"speaker":"Greg","startTime":2149.56,"endTime":2152.86,"body":"minimum, you move just a tiny"},{"speaker":"Greg","startTime":2149.56,"endTime":2152.86,"body":"bit, and the slope of a tangent"},{"speaker":"Greg","startTime":2152.86,"endTime":2160.87,"body":"to that parabola just goes"},{"speaker":"Greg","startTime":2152.86,"endTime":2160.87,"body":"shoots up way the heck up. Well,"},{"speaker":"Greg","startTime":2160.87,"endTime":2165.04,"body":"so how much the slope changes is"},{"speaker":"Greg","startTime":2160.87,"endTime":2165.04,"body":"the derivative of the"},{"speaker":"Greg","startTime":2165.04,"endTime":2168.07,"body":"derivative, which is the second"},{"speaker":"Greg","startTime":2165.04,"endTime":2168.07,"body":"derivative. And so by taking a"},{"speaker":"Greg","startTime":2168.07,"endTime":2171.04,"body":"second derivative, whether we do"},{"speaker":"Greg","startTime":2168.07,"endTime":2171.04,"body":"it analytically, which is how"},{"speaker":"Greg","startTime":2171.04,"endTime":2174.52,"body":"Fisher did it for simple"},{"speaker":"Greg","startTime":2171.04,"endTime":2174.52,"body":"functions, or we do it in some"},{"speaker":"Greg","startTime":2174.52,"endTime":2177.7,"body":"empirical way, we re chalk the"},{"speaker":"Greg","startTime":2174.52,"endTime":2177.7,"body":"heck out of that thing, and"},{"speaker":"Greg","startTime":2177.7,"endTime":2181.54,"body":"figure out how much change"},{"speaker":"Greg","startTime":2177.7,"endTime":2181.54,"body":"changes when you move, we get a"},{"speaker":"Greg","startTime":2181.54,"endTime":2185.68,"body":"sense of how stable our estimate"},{"speaker":"Greg","startTime":2181.54,"endTime":2185.68,"body":"is of a particular parameter."},{"speaker":"Greg","startTime":2185.83,"endTime":2190.39,"body":"And that's going to be used to"},{"speaker":"Greg","startTime":2185.83,"endTime":2190.39,"body":"inform us as to a standard error"},{"speaker":"Greg","startTime":2190.39,"endTime":2194.47,"body":"associated with the parameters."},{"speaker":"Greg","startTime":2190.39,"endTime":2194.47,"body":"So it is just gorgeous."},{"speaker":"Patrick","startTime":2194.56,"endTime":2197.65,"body":"It really, really is."},{"speaker":"Patrick","startTime":2194.56,"endTime":2197.65,"body":"And let's throw a couple of"},{"speaker":"Patrick","startTime":2197.65,"endTime":2201.1,"body":"terms out there. So that when"},{"speaker":"Patrick","startTime":2197.65,"endTime":2201.1,"body":"they come up at a cocktail"},{"speaker":"Patrick","startTime":2201.1,"endTime":2203.89,"body":"party, you can be intolerably"},{"speaker":"Patrick","startTime":2201.1,"endTime":2203.89,"body":"self righteous, because"},{"speaker":"Patrick","startTime":2203.89,"endTime":2207.34,"body":"remember, that's a theme of this"},{"speaker":"Patrick","startTime":2203.89,"endTime":2207.34,"body":"season, huge, huge goal, there"},{"speaker":"Patrick","startTime":2207.34,"endTime":2211.69,"body":"are three terms that you may"},{"speaker":"Patrick","startTime":2207.34,"endTime":2211.69,"body":"encounter when talking about"},{"speaker":"Patrick","startTime":2211.69,"endTime":2217.66,"body":"this a gradient, a hessayon, and"},{"speaker":"Patrick","startTime":2211.69,"endTime":2217.66,"body":"Fisher information matrix. All"},{"speaker":"Patrick","startTime":2217.66,"endTime":2221.74,"body":"the gradient matrix is is the"},{"speaker":"Patrick","startTime":2217.66,"endTime":2221.74,"body":"matrix of first derivatives."},{"speaker":"Patrick","startTime":2221.89,"endTime":2224.29,"body":"Alright, as we were talking"},{"speaker":"Patrick","startTime":2221.89,"endTime":2224.29,"body":"about trying to find that bottom"},{"speaker":"Patrick","startTime":2224.29,"endTime":2229.3,"body":"of the valley, the hessayon are"},{"speaker":"Patrick","startTime":2224.29,"endTime":2229.3,"body":"the second derivatives. And as"},{"speaker":"Patrick","startTime":2229.3,"endTime":2233.56,"body":"Greg just described, it's how"},{"speaker":"Patrick","startTime":2229.3,"endTime":2233.56,"body":"fast are those first derivatives"},{"speaker":"Patrick","startTime":2233.56,"endTime":2241.0,"body":"changing? No. So it's change in"},{"speaker":"Patrick","startTime":2233.56,"endTime":2241.0,"body":"the rate of change, right?"},{"speaker":"Patrick","startTime":2241.0,"endTime":2244.84,"body":"That's the hessayon. And then"},{"speaker":"Patrick","startTime":2241.0,"endTime":2244.84,"body":"the Fisher information matrix,"},{"speaker":"Patrick","startTime":2244.99,"endTime":2249.76,"body":"actually, is just minus one"},{"speaker":"Patrick","startTime":2244.99,"endTime":2249.76,"body":"times the Halcyon. Fischer"},{"speaker":"Patrick","startTime":2249.76,"endTime":2253.66,"body":"derive this as part of his early"},{"speaker":"Patrick","startTime":2249.76,"endTime":2253.66,"body":"work that when Greg was at AC,"},{"speaker":"Patrick","startTime":2253.66,"endTime":2258.19,"body":"DC, I was at Van Halen, he was"},{"speaker":"Patrick","startTime":2253.66,"endTime":2258.19,"body":"inventing maximum likelihood,"},{"speaker":"Patrick","startTime":2259.09,"endTime":2262.51,"body":"that is a matrix of second"},{"speaker":"Patrick","startTime":2259.09,"endTime":2262.51,"body":"derivatives that has been"},{"speaker":"Patrick","startTime":2262.51,"endTime":2265.54,"body":"multiplied by negative one. And"},{"speaker":"Patrick","startTime":2262.51,"endTime":2265.54,"body":"what that negative one does is"},{"speaker":"Patrick","startTime":2265.54,"endTime":2268.03,"body":"the second derivatives, by"},{"speaker":"Patrick","startTime":2265.54,"endTime":2268.03,"body":"definition are negative, and it"},{"speaker":"Patrick","startTime":2268.03,"endTime":2272.44,"body":"simply strips off the negative."},{"speaker":"Patrick","startTime":2268.03,"endTime":2272.44,"body":"And then the last one, you take"},{"speaker":"Patrick","startTime":2272.44,"endTime":2276.52,"body":"the inverse of the Fisher"},{"speaker":"Patrick","startTime":2272.44,"endTime":2276.52,"body":"information matrix, and the"},{"speaker":"Patrick","startTime":2276.52,"endTime":2280.84,"body":"diagonal elements are the"},{"speaker":"Patrick","startTime":2276.52,"endTime":2280.84,"body":"maximum likelihood estimate of"},{"speaker":"Patrick","startTime":2280.84,"endTime":2285.01,"body":"the variance of the parameter"},{"speaker":"Patrick","startTime":2280.84,"endTime":2285.01,"body":"estimates. Nice. What do we do"},{"speaker":"Patrick","startTime":2285.01,"endTime":2288.1,"body":"with that we take the square"},{"speaker":"Patrick","startTime":2285.01,"endTime":2288.1,"body":"root and make it a standard"},{"speaker":"Patrick","startTime":2288.1,"endTime":2293.17,"body":"deviation. And that is our"},{"speaker":"Patrick","startTime":2288.1,"endTime":2293.17,"body":"standard error. For every"},{"speaker":"Patrick","startTime":2293.17,"endTime":2298.09,"body":"parameter, we estimate the"},{"speaker":"Patrick","startTime":2293.17,"endTime":2298.09,"body":"square root of the inverse of"},{"speaker":"Patrick","startTime":2298.09,"endTime":2301.48,"body":"the Fisher information matrix"},{"speaker":"Patrick","startTime":2298.09,"endTime":2301.48,"body":"are our maximum likelihood"},{"speaker":"Patrick","startTime":2301.48,"endTime":2304.57,"body":"standard errors. It is"},{"speaker":"Patrick","startTime":2301.48,"endTime":2304.57,"body":"absolutely stunning,"},{"speaker":"Greg","startTime":2304.69,"endTime":2308.26,"body":"gorgeous, and it just"},{"speaker":"Greg","startTime":2304.69,"endTime":2308.26,"body":"really makes me feel even worse"},{"speaker":"Greg","startTime":2308.26,"endTime":2309.1,"body":"about my 20s."},{"speaker":"Patrick","startTime":2310.9,"endTime":2313.06,"body":"There are a couple of"},{"speaker":"Patrick","startTime":2310.9,"endTime":2313.06,"body":"interesting things to think"},{"speaker":"Patrick","startTime":2313.06,"endTime":2316.45,"body":"about for traditional maximum"},{"speaker":"Patrick","startTime":2313.06,"endTime":2316.45,"body":"likelihood. Now, I'm going to"},{"speaker":"Patrick","startTime":2316.45,"endTime":2319.03,"body":"stress that because this can be"},{"speaker":"Patrick","startTime":2316.45,"endTime":2319.03,"body":"applied in a lot of different"},{"speaker":"Patrick","startTime":2319.03,"endTime":2322.99,"body":"settings for traditional maximum"},{"speaker":"Patrick","startTime":2319.03,"endTime":2322.99,"body":"likelihood, we assumed that our"},{"speaker":"Patrick","startTime":2322.99,"endTime":2329.77,"body":"variables are continuous, normal"},{"speaker":"Patrick","startTime":2322.99,"endTime":2329.77,"body":"and independent. Well, why do we"},{"speaker":"Patrick","startTime":2329.8,"endTime":2333.22,"body":"assume that for maximum"},{"speaker":"Patrick","startTime":2329.8,"endTime":2333.22,"body":"likelihood? Well, continuity, we"},{"speaker":"Patrick","startTime":2333.22,"endTime":2337.3,"body":"move up and down that number"},{"speaker":"Patrick","startTime":2333.22,"endTime":2337.3,"body":"line to paint out the smooth"},{"speaker":"Patrick","startTime":2337.33,"endTime":2341.56,"body":"curve? Normal, what we can't"},{"speaker":"Patrick","startTime":2337.33,"endTime":2341.56,"body":"compute the likelihood if we"},{"speaker":"Patrick","startTime":2341.56,"endTime":2345.76,"body":"don't know what the shape of the"},{"speaker":"Patrick","startTime":2341.56,"endTime":2345.76,"body":"distribution is, or a fisher"},{"speaker":"Patrick","startTime":2345.76,"endTime":2352.51,"body":"declares, I state that it is"},{"speaker":"Patrick","startTime":2345.76,"endTime":2352.51,"body":"normal. And that allows us to"},{"speaker":"Patrick","startTime":2352.51,"endTime":2356.62,"body":"calculate the likelihood. Why do"},{"speaker":"Patrick","startTime":2352.51,"endTime":2356.62,"body":"we assume independence? Because"},{"speaker":"Patrick","startTime":2356.62,"endTime":2359.38,"body":"we take these products of"},{"speaker":"Patrick","startTime":2356.62,"endTime":2359.38,"body":"likelihoods to get the joint"},{"speaker":"Patrick","startTime":2359.38,"endTime":2362.17,"body":"likelihood. These are the"},{"speaker":"Patrick","startTime":2359.38,"endTime":2362.17,"body":"reasons that we make those"},{"speaker":"Patrick","startTime":2362.17,"endTime":2362.89,"body":"assumptions."},{"speaker":"Greg","startTime":2362.92,"endTime":2365.17,"body":"So when Patrick said"},{"speaker":"Greg","startTime":2362.92,"endTime":2365.17,"body":"earlier that, you know we were"},{"speaker":"Greg","startTime":2365.17,"endTime":2369.79,"body":"going to put this curve over"},{"speaker":"Greg","startTime":2365.17,"endTime":2369.79,"body":"your head, it was decided it was"},{"speaker":"Greg","startTime":2369.79,"endTime":2372.61,"body":"decided what the shape of the"},{"speaker":"Greg","startTime":2369.79,"endTime":2372.61,"body":"curve was going to be. For"},{"speaker":"Greg","startTime":2372.61,"endTime":2375.43,"body":"reasons we actually talked about"},{"speaker":"Greg","startTime":2372.61,"endTime":2375.43,"body":"last summer, a lot of the"},{"speaker":"Greg","startTime":2375.43,"endTime":2378.55,"body":"popularity associated with the"},{"speaker":"Greg","startTime":2375.43,"endTime":2378.55,"body":"normal curve. A lot of"},{"speaker":"Greg","startTime":2378.55,"endTime":2381.85,"body":"observations in nature that"},{"speaker":"Greg","startTime":2378.55,"endTime":2381.85,"body":"subscribe to the normal normal"},{"speaker":"Greg","startTime":2381.85,"endTime":2384.94,"body":"curve was hugely popular. You"},{"speaker":"Greg","startTime":2381.85,"endTime":2384.94,"body":"know, if some other curve had"},{"speaker":"Greg","startTime":2384.94,"endTime":2389.11,"body":"been all the rage back in the"},{"speaker":"Greg","startTime":2384.94,"endTime":2389.11,"body":"late 1800s, early 1900s, then"},{"speaker":"Greg","startTime":2389.14,"endTime":2391.42,"body":"maybe different decisions would"},{"speaker":"Greg","startTime":2389.14,"endTime":2391.42,"body":"have been made, but the normal"},{"speaker":"Greg","startTime":2391.42,"endTime":2394.69,"body":"curve was chosen. And there are"},{"speaker":"Greg","startTime":2391.42,"endTime":2394.69,"body":"a lot of great things about the"},{"speaker":"Greg","startTime":2394.69,"endTime":2397.09,"body":"normal curve and as Patrick"},{"speaker":"Greg","startTime":2394.69,"endTime":2397.09,"body":"said, that serves as the"},{"speaker":"Greg","startTime":2397.09,"endTime":2398.95,"body":"foundation for so much of what"},{"speaker":"Greg","startTime":2397.09,"endTime":2398.95,"body":"we do,"},{"speaker":"Patrick","startTime":2399.04,"endTime":2401.68,"body":"and there was more"},{"speaker":"Patrick","startTime":2399.04,"endTime":2401.68,"body":"motivation for doing that, as"},{"speaker":"Patrick","startTime":2401.68,"endTime":2405.43,"body":"you already alluded to, a lot of"},{"speaker":"Patrick","startTime":2401.68,"endTime":2405.43,"body":"things in the world are normally"},{"speaker":"Patrick","startTime":2405.43,"endTime":2408.76,"body":"distributed or near normally"},{"speaker":"Patrick","startTime":2405.43,"endTime":2408.76,"body":"distributed. And given"},{"speaker":"Patrick","startTime":2408.76,"endTime":2411.73,"body":"everything that we do in our day"},{"speaker":"Patrick","startTime":2408.76,"endTime":2411.73,"body":"job, we're trying to make"},{"speaker":"Patrick","startTime":2411.73,"endTime":2414.88,"body":"approximations to a more"},{"speaker":"Patrick","startTime":2411.73,"endTime":2414.88,"body":"complicated system. And"},{"speaker":"Patrick","startTime":2414.88,"endTime":2418.66,"body":"normality is not about"},{"speaker":"Patrick","startTime":2414.88,"endTime":2418.66,"body":"approximation. But it is non"},{"speaker":"Patrick","startTime":2418.66,"endTime":2424.51,"body":"trivial. When Fisher was doing"},{"speaker":"Patrick","startTime":2418.66,"endTime":2424.51,"body":"these derivations by hand, on"},{"speaker":"Patrick","startTime":2424.54,"endTime":2430.69,"body":"reams of paper, the normal is an"},{"speaker":"Patrick","startTime":2424.54,"endTime":2430.69,"body":"easier, more tractable"},{"speaker":"Patrick","startTime":2430.69,"endTime":2432.46,"body":"distribution to work with."},{"speaker":"Patrick","startTime":2439.51,"endTime":2442.78,"body":"So part of it is it does reflect"},{"speaker":"Patrick","startTime":2439.51,"endTime":2442.78,"body":"a lot of what's in the world"},{"speaker":"Patrick","startTime":2442.78,"endTime":2446.74,"body":"around us. But the other part is"},{"speaker":"Patrick","startTime":2442.78,"endTime":2446.74,"body":"simplified the math at a time"},{"speaker":"Patrick","startTime":2446.83,"endTime":2451.57,"body":"where you had to simplify the"},{"speaker":"Patrick","startTime":2446.83,"endTime":2451.57,"body":"math, right? So for the moment,"},{"speaker":"Patrick","startTime":2451.6,"endTime":2455.83,"body":"let's assume that we are meeting"},{"speaker":"Patrick","startTime":2451.6,"endTime":2455.83,"body":"the underlying assumptions, when"},{"speaker":"Patrick","startTime":2455.83,"endTime":2460.36,"body":"we meet those describe to us"},{"speaker":"Patrick","startTime":2455.83,"endTime":2460.36,"body":"some of the remarkable"},{"speaker":"Patrick","startTime":2460.36,"endTime":2463.81,"body":"properties that maximum"},{"speaker":"Patrick","startTime":2460.36,"endTime":2463.81,"body":"likelihood gives us in these"},{"speaker":"Patrick","startTime":2463.81,"endTime":2464.95,"body":"parameter estimates,"},{"speaker":"Greg","startTime":2464.98,"endTime":2469.0,"body":"right? Well, the big three"},{"speaker":"Greg","startTime":2464.98,"endTime":2469.0,"body":"are unbiasness, consistency and"},{"speaker":"Greg","startTime":2469.0,"endTime":2474.37,"body":"efficiency. And the idea of"},{"speaker":"Greg","startTime":2469.0,"endTime":2474.37,"body":"unbiasness is that that estimate"},{"speaker":"Greg","startTime":2474.4,"endTime":2477.7,"body":"will not have a tendency to be"},{"speaker":"Greg","startTime":2474.4,"endTime":2477.7,"body":"to the left, it won't have a"},{"speaker":"Greg","startTime":2477.7,"endTime":2480.97,"body":"tendency to be to the right that"},{"speaker":"Greg","startTime":2477.7,"endTime":2480.97,"body":"as sample sizes get larger, it"},{"speaker":"Greg","startTime":2480.97,"endTime":2483.49,"body":"will be spot on. So it will be"},{"speaker":"Greg","startTime":2480.97,"endTime":2483.49,"body":"an unbiased estimate of the"},{"speaker":"Greg","startTime":2483.49,"endTime":2487.87,"body":"actual population parameter."},{"speaker":"Greg","startTime":2483.49,"endTime":2487.87,"body":"Consistency means that the"},{"speaker":"Greg","startTime":2487.87,"endTime":2490.69,"body":"quality of that estimate gets"},{"speaker":"Greg","startTime":2487.87,"endTime":2490.69,"body":"better and better and better as"},{"speaker":"Greg","startTime":2490.69,"endTime":2493.18,"body":"sample size gets bigger. Another"},{"speaker":"Greg","startTime":2490.69,"endTime":2493.18,"body":"way of saying that is that your"},{"speaker":"Greg","startTime":2493.18,"endTime":2497.44,"body":"standard error start shrinking"},{"speaker":"Greg","startTime":2493.18,"endTime":2497.44,"body":"tightening up around that. And"},{"speaker":"Greg","startTime":2497.47,"endTime":2501.04,"body":"an efficient estimator means"},{"speaker":"Greg","startTime":2497.47,"endTime":2501.04,"body":"that it is the one that is the"},{"speaker":"Greg","startTime":2501.04,"endTime":2504.19,"body":"best bang for your sample size"},{"speaker":"Greg","startTime":2501.04,"endTime":2504.19,"body":"Buck like you can't get"},{"speaker":"Greg","startTime":2504.19,"endTime":2506.77,"body":"something with a smaller"},{"speaker":"Greg","startTime":2504.19,"endTime":2506.77,"body":"standard error for the price of"},{"speaker":"Greg","startTime":2506.77,"endTime":2509.95,"body":"that sample size than you can"},{"speaker":"Greg","startTime":2506.77,"endTime":2509.95,"body":"with a maximum likelihood"},{"speaker":"Greg","startTime":2509.95,"endTime":2514.45,"body":"process. So unbiasness,"},{"speaker":"Greg","startTime":2509.95,"endTime":2514.45,"body":"consistency and efficiency are"},{"speaker":"Greg","startTime":2514.48,"endTime":2517.66,"body":"hallmarks of the maximum"},{"speaker":"Greg","startTime":2514.48,"endTime":2517.66,"body":"likelihood estimation framework."},{"speaker":"Patrick","startTime":2517.69,"endTime":2521.68,"body":"And one thing that I"},{"speaker":"Patrick","startTime":2517.69,"endTime":2521.68,"body":"love is all of those properties"},{"speaker":"Patrick","startTime":2521.71,"endTime":2525.01,"body":"that are associated with"},{"speaker":"Patrick","startTime":2521.71,"endTime":2525.01,"body":"individual parameter estimates"},{"speaker":"Patrick","startTime":2525.1,"endTime":2530.05,"body":"also apply to compounds have"},{"speaker":"Patrick","startTime":2525.1,"endTime":2530.05,"body":"parameter estimates. And you"},{"speaker":"Patrick","startTime":2530.05,"endTime":2532.54,"body":"might say to yourself while"},{"speaker":"Patrick","startTime":2530.05,"endTime":2532.54,"body":"you're cooking dinner right now,"},{"speaker":"Patrick","startTime":2532.57,"endTime":2536.02,"body":"why would I ever make a compound"},{"speaker":"Patrick","startTime":2532.57,"endTime":2536.02,"body":"estimate of multiple maximum"},{"speaker":"Patrick","startTime":2536.02,"endTime":2539.17,"body":"likelihood parameters? That"},{"speaker":"Patrick","startTime":2536.02,"endTime":2539.17,"body":"seems silly? Think about"},{"speaker":"Patrick","startTime":2539.17,"endTime":2544.0,"body":"mediation, you have X to Y to Z,"},{"speaker":"Patrick","startTime":2539.17,"endTime":2544.0,"body":"and there's an x to y"},{"speaker":"Patrick","startTime":2544.03,"endTime":2547.36,"body":"coefficient and a y to z"},{"speaker":"Patrick","startTime":2544.03,"endTime":2547.36,"body":"coefficient? How do we estimate"},{"speaker":"Patrick","startTime":2547.36,"endTime":2550.93,"body":"that mediated effect, you take"},{"speaker":"Patrick","startTime":2547.36,"endTime":2550.93,"body":"the product of those two"},{"speaker":"Patrick","startTime":2550.93,"endTime":2554.08,"body":"parameter estimates? Well, if"},{"speaker":"Patrick","startTime":2550.93,"endTime":2554.08,"body":"those are maximum likelihood"},{"speaker":"Patrick","startTime":2554.08,"endTime":2557.8,"body":"parameter estimates, the product"},{"speaker":"Patrick","startTime":2554.08,"endTime":2557.8,"body":"is also a maximum likelihood"},{"speaker":"Patrick","startTime":2557.8,"endTime":2561.91,"body":"estimate. We take sums, we look"},{"speaker":"Patrick","startTime":2557.8,"endTime":2561.91,"body":"at Conditional values, we probe"},{"speaker":"Patrick","startTime":2561.91,"endTime":2567.88,"body":"interactions, we do this all the"},{"speaker":"Patrick","startTime":2561.91,"endTime":2567.88,"body":"time. So this scales up in ways"},{"speaker":"Patrick","startTime":2567.88,"endTime":2570.58,"body":"that are really quite"},{"speaker":"Patrick","startTime":2567.88,"endTime":2570.58,"body":"remarkable. One way that we"},{"speaker":"Patrick","startTime":2570.58,"endTime":2573.85,"body":"haven't talked about yet is not"},{"speaker":"Patrick","startTime":2570.58,"endTime":2573.85,"body":"only do we get these wonderful"},{"speaker":"Patrick","startTime":2573.85,"endTime":2577.57,"body":"parameter estimates and"},{"speaker":"Patrick","startTime":2573.85,"endTime":2577.57,"body":"asymptotic standard errors, but"},{"speaker":"Patrick","startTime":2577.57,"endTime":2580.09,"body":"we're able to do model"},{"speaker":"Patrick","startTime":2577.57,"endTime":2580.09,"body":"comparisons,"},{"speaker":"Greg","startTime":2580.12,"endTime":2583.39,"body":"I love model comparisons."},{"speaker":"Greg","startTime":2580.12,"endTime":2583.39,"body":"And I love that that comes out"},{"speaker":"Greg","startTime":2583.39,"endTime":2586.09,"body":"of all of this. Now in the least"},{"speaker":"Greg","startTime":2583.39,"endTime":2586.09,"body":"squares world, we talk about"},{"speaker":"Greg","startTime":2586.09,"endTime":2589.03,"body":"model comparisons to we talk"},{"speaker":"Greg","startTime":2586.09,"endTime":2589.03,"body":"about a little bit differently,"},{"speaker":"Greg","startTime":2589.24,"endTime":2594.61,"body":"usually in terms of reduction in"},{"speaker":"Greg","startTime":2589.24,"endTime":2594.61,"body":"sums of squares, right R squared"},{"speaker":"Greg","startTime":2594.61,"endTime":2598.12,"body":"change, when we for example, in"},{"speaker":"Greg","startTime":2594.61,"endTime":2598.12,"body":"regression, add three more"},{"speaker":"Greg","startTime":2598.12,"endTime":2601.51,"body":"predictors, is our model better,"},{"speaker":"Greg","startTime":2598.12,"endTime":2601.51,"body":"what we're really asking is"},{"speaker":"Greg","startTime":2601.51,"endTime":2606.82,"body":"whether or not we have reduced"},{"speaker":"Greg","startTime":2601.51,"endTime":2606.82,"body":"the error sum of squares. And we"},{"speaker":"Greg","startTime":2606.82,"endTime":2610.03,"body":"have significance tests"},{"speaker":"Greg","startTime":2606.82,"endTime":2610.03,"body":"associated with delta r squared."},{"speaker":"Greg","startTime":2610.03,"endTime":2612.49,"body":"And that's how we talk about"},{"speaker":"Greg","startTime":2610.03,"endTime":2612.49,"body":"model comparison in that"},{"speaker":"Greg","startTime":2612.49,"endTime":2616.18,"body":"particular world. In the maximum"},{"speaker":"Greg","startTime":2612.49,"endTime":2616.18,"body":"likelihood world, the idea is"},{"speaker":"Greg","startTime":2616.18,"endTime":2620.53,"body":"that if we have two models whose"},{"speaker":"Greg","startTime":2616.18,"endTime":2620.53,"body":"goal it is to explain why the"},{"speaker":"Greg","startTime":2620.53,"endTime":2624.28,"body":"data are the way that they are,"},{"speaker":"Greg","startTime":2620.53,"endTime":2624.28,"body":"the better models should yield"},{"speaker":"Greg","startTime":2624.28,"endTime":2629.62,"body":"an overall higher likelihood"},{"speaker":"Greg","startTime":2624.28,"endTime":2629.62,"body":"higher log likelihood, lower"},{"speaker":"Greg","startTime":2629.62,"endTime":2633.46,"body":"negative two log likelihood. And"},{"speaker":"Greg","startTime":2629.62,"endTime":2633.46,"body":"so I might have one model that"},{"speaker":"Greg","startTime":2633.46,"endTime":2636.67,"body":"has one will say negative two"},{"speaker":"Greg","startTime":2633.46,"endTime":2636.67,"body":"log likelihood for its"},{"speaker":"Greg","startTime":2636.67,"endTime":2639.58,"body":"observations, another model that"},{"speaker":"Greg","startTime":2636.67,"endTime":2639.58,"body":"has its negative two log"},{"speaker":"Greg","startTime":2639.58,"endTime":2642.64,"body":"likelihood for its observations."},{"speaker":"Greg","startTime":2639.58,"endTime":2642.64,"body":"And I want to make comparisons"},{"speaker":"Greg","startTime":2642.64,"endTime":2645.52,"body":"between these two. Well, under"},{"speaker":"Greg","startTime":2642.64,"endTime":2645.52,"body":"the right conditions, conditions"},{"speaker":"Greg","startTime":2645.52,"endTime":2648.37,"body":"that Patrick and I have talked"},{"speaker":"Greg","startTime":2645.52,"endTime":2648.37,"body":"about before here, if these"},{"speaker":"Greg","startTime":2648.37,"endTime":2653.23,"body":"models are nested, if one is a"},{"speaker":"Greg","startTime":2648.37,"endTime":2653.23,"body":"special case of the other model,"},{"speaker":"Greg","startTime":2653.53,"endTime":2657.1,"body":"then we can actually test the"},{"speaker":"Greg","startTime":2653.53,"endTime":2657.1,"body":"difference between those"},{"speaker":"Greg","startTime":2657.28,"endTime":2661.3,"body":"negative to log likelihoods and"},{"speaker":"Greg","startTime":2657.28,"endTime":2661.3,"body":"that in and of itself becomes a"},{"speaker":"Greg","startTime":2661.33,"endTime":2662.53,"body":"testable quantity."},{"speaker":"Patrick","startTime":2662.71,"endTime":2666.25,"body":"And again, in getting"},{"speaker":"Patrick","startTime":2662.71,"endTime":2666.25,"body":"an insight in where some of our"},{"speaker":"Patrick","startTime":2666.25,"endTime":2670.33,"body":"terminology has come from"},{"speaker":"Patrick","startTime":2666.25,"endTime":2670.33,"body":"historically, we talk about"},{"speaker":"Patrick","startTime":2670.36,"endTime":2675.34,"body":"likelihood ratio tests. The lot"},{"speaker":"Patrick","startTime":2670.36,"endTime":2675.34,"body":"of you have had this in class,"},{"speaker":"Patrick","startTime":2675.43,"endTime":2678.64,"body":"you've done it yourself. You've"},{"speaker":"Patrick","startTime":2675.43,"endTime":2678.64,"body":"read it in an article, and they"},{"speaker":"Patrick","startTime":2678.64,"endTime":2682.69,"body":"say we use the likelihood ratio"},{"speaker":"Patrick","startTime":2678.64,"endTime":2682.69,"body":"test to compare this and that."},{"speaker":"Patrick","startTime":2682.99,"endTime":2687.31,"body":"Well, that's what we're doing."},{"speaker":"Patrick","startTime":2682.99,"endTime":2687.31,"body":"We're comparing the likelihoods"},{"speaker":"Patrick","startTime":2687.43,"endTime":2690.91,"body":"and one way that you can do"},{"speaker":"Patrick","startTime":2687.43,"endTime":2690.91,"body":"that. And this is moving back"},{"speaker":"Patrick","startTime":2690.91,"endTime":2695.74,"body":"and forth between exponents and"},{"speaker":"Patrick","startTime":2690.91,"endTime":2695.74,"body":"natural logs, is you can take a"},{"speaker":"Patrick","startTime":2695.74,"endTime":2700.96,"body":"ratio of two likelihoods and"},{"speaker":"Patrick","startTime":2695.74,"endTime":2700.96,"body":"that is the law. Could ratio"},{"speaker":"Patrick","startTime":2700.96,"endTime":2703.81,"body":"test. So that's where that"},{"speaker":"Patrick","startTime":2700.96,"endTime":2703.81,"body":"terminology comes from."},{"speaker":"Greg","startTime":2703.84,"endTime":2706.69,"body":"Yeah, it's exactly right."},{"speaker":"Greg","startTime":2703.84,"endTime":2706.69,"body":"You know, I don't tend to think"},{"speaker":"Greg","startTime":2706.69,"endTime":2710.02,"body":"about things as likelihood ratio"},{"speaker":"Greg","startTime":2706.69,"endTime":2710.02,"body":"tests, but absolutely they are."},{"speaker":"Greg","startTime":2710.02,"endTime":2713.41,"body":"And you can even say, LR t if"},{"speaker":"Greg","startTime":2710.02,"endTime":2713.41,"body":"you're one of the cool kids. But"},{"speaker":"Greg","startTime":2713.41,"endTime":2716.83,"body":"I always think about it in terms"},{"speaker":"Greg","startTime":2713.41,"endTime":2716.83,"body":"of logarithms. So the logarithm"},{"speaker":"Greg","startTime":2716.83,"endTime":2719.59,"body":"of a ratio just becomes the"},{"speaker":"Greg","startTime":2716.83,"endTime":2719.59,"body":"difference between two things."},{"speaker":"Greg","startTime":2719.59,"endTime":2722.35,"body":"And I like that because the"},{"speaker":"Greg","startTime":2719.59,"endTime":2722.35,"body":"least squares part of my brain"},{"speaker":"Greg","startTime":2722.35,"endTime":2725.5,"body":"thinks about differences in our"},{"speaker":"Greg","startTime":2722.35,"endTime":2725.5,"body":"squares or differences in sums"},{"speaker":"Greg","startTime":2725.5,"endTime":2728.86,"body":"of squares. In my maximum"},{"speaker":"Greg","startTime":2725.5,"endTime":2728.86,"body":"likelihood brain thinks about"},{"speaker":"Greg","startTime":2728.86,"endTime":2731.56,"body":"things in terms of differences"},{"speaker":"Greg","startTime":2728.86,"endTime":2731.56,"body":"between negative two log"},{"speaker":"Greg","startTime":2731.56,"endTime":2734.77,"body":"likelihoods. And that happens to"},{"speaker":"Greg","startTime":2731.56,"endTime":2734.77,"body":"be a nice metric, because that"},{"speaker":"Greg","startTime":2734.77,"endTime":2737.62,"body":"under the right circumstances"},{"speaker":"Greg","startTime":2734.77,"endTime":2737.62,"body":"can map onto things like chi"},{"speaker":"Greg","startTime":2737.62,"endTime":2740.68,"body":"square distributions, things"},{"speaker":"Greg","startTime":2737.62,"endTime":2740.68,"body":"where we know sort of how big"},{"speaker":"Greg","startTime":2740.68,"endTime":2742.69,"body":"that has to be to impress us."},{"speaker":"Patrick","startTime":2742.75,"endTime":2745.81,"body":"So let's think a little"},{"speaker":"Patrick","startTime":2742.75,"endTime":2745.81,"body":"bit then about the Kelvin ball"},{"speaker":"Patrick","startTime":2745.81,"endTime":2749.2,"body":"rules that Fisher came up with,"},{"speaker":"Patrick","startTime":2745.81,"endTime":2749.2,"body":"right? You don't get this all"},{"speaker":"Patrick","startTime":2749.2,"endTime":2750.01,"body":"for free. That's"},{"speaker":"Greg","startTime":2751.33,"endTime":2753.67,"body":"Is there a Reaper coming?"},{"speaker":"Greg","startTime":2751.33,"endTime":2753.67,"body":"It's less of a Reaper and more"},{"speaker":"Patrick","startTime":2753.67,"endTime":2756.85,"body":"like a bouncer? Okay."},{"speaker":"Patrick","startTime":2753.67,"endTime":2756.85,"body":"Everything that we've talked"},{"speaker":"Patrick","startTime":2756.85,"endTime":2762.49,"body":"about so far applies under a"},{"speaker":"Patrick","startTime":2756.85,"endTime":2762.49,"body":"certain set of conditions. A lot"},{"speaker":"Patrick","startTime":2762.49,"endTime":2765.52,"body":"of these we've talked about"},{"speaker":"Patrick","startTime":2762.49,"endTime":2765.52,"body":"somewhat implicitly a few"},{"speaker":"Patrick","startTime":2765.52,"endTime":2769.42,"body":"explicitly, but let's think"},{"speaker":"Patrick","startTime":2765.52,"endTime":2769.42,"body":"about the obvious ones. First,"},{"speaker":"Patrick","startTime":2769.45,"endTime":2773.56,"body":"we assume independence,"},{"speaker":"Patrick","startTime":2769.45,"endTime":2773.56,"body":"continuity, and multivariate"},{"speaker":"Patrick","startTime":2773.56,"endTime":2776.5,"body":"normality. Those all have to"},{"speaker":"Patrick","startTime":2773.56,"endTime":2776.5,"body":"hold because of what we talked"},{"speaker":"Patrick","startTime":2776.5,"endTime":2780.52,"body":"about earlier, right? Those are"},{"speaker":"Patrick","startTime":2776.5,"endTime":2780.52,"body":"obvious, a little less obvious,"},{"speaker":"Patrick","startTime":2780.52,"endTime":2785.08,"body":"and one that has no real answer"},{"speaker":"Patrick","startTime":2780.52,"endTime":2785.08,"body":"is we need a sufficiently large"},{"speaker":"Patrick","startTime":2785.08,"endTime":2789.55,"body":"sample size. In order for those"},{"speaker":"Patrick","startTime":2785.08,"endTime":2789.55,"body":"asymptotic derivations to kick"},{"speaker":"Patrick","startTime":2789.55,"endTime":2795.34,"body":"in, I dare anyone to ask us what"},{"speaker":"Patrick","startTime":2789.55,"endTime":2795.34,"body":"that sample size is. Nobody"},{"speaker":"Patrick","startTime":2795.34,"endTime":2795.94,"body":"knows"},{"speaker":"Greg","startTime":2795.97,"endTime":2798.73,"body":"it is the best kept secret"},{"speaker":"Greg","startTime":2795.97,"endTime":2798.73,"body":"in all of statistics."},{"speaker":"Patrick","startTime":2799.93,"endTime":2804.73,"body":"We often focus on"},{"speaker":"Patrick","startTime":2799.93,"endTime":2804.73,"body":"sample size, just in terms of"},{"speaker":"Patrick","startTime":2804.73,"endTime":2808.93,"body":"power. But we really, really"},{"speaker":"Patrick","startTime":2804.73,"endTime":2808.93,"body":"need to pay attention to sample"},{"speaker":"Patrick","startTime":2808.93,"endTime":2813.58,"body":"size in terms of have we got the"},{"speaker":"Patrick","startTime":2808.93,"endTime":2813.58,"body":"ticket to get on the maximum"},{"speaker":"Patrick","startTime":2813.58,"endTime":2823.03,"body":"likelihood ride. That is, we"},{"speaker":"Patrick","startTime":2813.58,"endTime":2823.03,"body":"have to have a large enough n,"},{"speaker":"Patrick","startTime":2823.12,"endTime":2827.02,"body":"where all of these properties"},{"speaker":"Patrick","startTime":2823.12,"endTime":2827.02,"body":"come on board. But those are the"},{"speaker":"Patrick","startTime":2827.02,"endTime":2831.01,"body":"obvious Calvin Ball rules. There"},{"speaker":"Patrick","startTime":2827.02,"endTime":2831.01,"body":"are a couple of other trickier"},{"speaker":"Patrick","startTime":2831.01,"endTime":2836.38,"body":"ones that are less obvious, that"},{"speaker":"Patrick","startTime":2831.01,"endTime":2836.38,"body":"can really start to eat away at"},{"speaker":"Patrick","startTime":2836.38,"endTime":2841.51,"body":"you. And one of the big ones is"},{"speaker":"Patrick","startTime":2836.38,"endTime":2841.51,"body":"it assumes your model is"},{"speaker":"Patrick","startTime":2841.51,"endTime":2843.07,"body":"properly specified."},{"speaker":"Greg","startTime":2844.24,"endTime":2848.26,"body":"Wait, what Didn't we say"},{"speaker":"Greg","startTime":2844.24,"endTime":2848.26,"body":"all models are wrong. But"},{"speaker":"Greg","startTime":2848.26,"endTime":2851.56,"body":"summary. Wait a minute. Yeah. So"},{"speaker":"Greg","startTime":2848.26,"endTime":2851.56,"body":"wait a minute, that's the fine"},{"speaker":"Greg","startTime":2851.56,"endTime":2852.04,"body":"print. So"},{"speaker":"Patrick","startTime":2852.04,"endTime":2856.78,"body":"here's the fine print,"},{"speaker":"Patrick","startTime":2852.04,"endTime":2856.78,"body":"we just described all the truly"},{"speaker":"Patrick","startTime":2856.78,"endTime":2861.19,"body":"amazing things about maximum"},{"speaker":"Patrick","startTime":2856.78,"endTime":2861.19,"body":"likelihood. And now we're going"},{"speaker":"Patrick","startTime":2861.19,"endTime":2864.85,"body":"to go back to the office in the"},{"speaker":"Patrick","startTime":2861.19,"endTime":2864.85,"body":"morning, and we are going to"},{"speaker":"Patrick","startTime":2864.85,"endTime":2869.83,"body":"take our finite sample that is"},{"speaker":"Patrick","startTime":2864.85,"endTime":2869.83,"body":"not normally distributed, and"},{"speaker":"Patrick","startTime":2869.83,"endTime":2872.05,"body":"fit an incorrect model to it."},{"speaker":"Greg","startTime":2873.37,"endTime":2874.81,"body":"What could possibly go"},{"speaker":"Patrick","startTime":2877.0,"endTime":2879.55,"body":"by I gotta go pick up"},{"speaker":"Patrick","startTime":2877.0,"endTime":2879.55,"body":"the kids."},{"speaker":"Greg","startTime":2879.64,"endTime":2882.31,"body":"So for all of the beauty"},{"speaker":"Greg","startTime":2879.64,"endTime":2882.31,"body":"and elegance of maximum"},{"speaker":"Greg","startTime":2882.31,"endTime":2885.13,"body":"likelihood, and it is a"},{"speaker":"Greg","startTime":2882.31,"endTime":2885.13,"body":"workhorse, right? I mean, it's"},{"speaker":"Greg","startTime":2885.13,"endTime":2890.77,"body":"in everything that you and I do"},{"speaker":"Greg","startTime":2885.13,"endTime":2890.77,"body":"on a day to day basis. There is"},{"speaker":"Greg","startTime":2890.77,"endTime":2895.15,"body":"that fine print. And it means"},{"speaker":"Greg","startTime":2890.77,"endTime":2895.15,"body":"that there's an opportunity for"},{"speaker":"Greg","startTime":2895.36,"endTime":2899.38,"body":"a understanding how bad things"},{"speaker":"Greg","startTime":2895.36,"endTime":2899.38,"body":"can get, which sort of"},{"speaker":"Greg","startTime":2899.38,"endTime":2902.59,"body":"describes, you know, 20 or 30"},{"speaker":"Greg","startTime":2899.38,"endTime":2902.59,"body":"years of simulation research."},{"speaker":"Greg","startTime":2902.59,"endTime":2904.9,"body":"What happens if this isn't"},{"speaker":"Greg","startTime":2902.59,"endTime":2904.9,"body":"right? What happens if this"},{"speaker":"Greg","startTime":2904.9,"endTime":2905.89,"body":"isn't right? I'm sorry,"},{"speaker":"Patrick","startTime":2905.89,"endTime":2909.01,"body":"that just described my"},{"speaker":"Patrick","startTime":2905.89,"endTime":2909.01,"body":"dissertation. So thank you for"},{"speaker":"Patrick","startTime":2909.01,"endTime":2909.37,"body":"that."},{"speaker":"Greg","startTime":2909.43,"endTime":2914.77,"body":"I knew that it did,"},{"speaker":"Greg","startTime":2909.43,"endTime":2914.77,"body":"actually. But then also an"},{"speaker":"Greg","startTime":2914.77,"endTime":2918.07,"body":"opportunity, how can we make it"},{"speaker":"Greg","startTime":2914.77,"endTime":2918.07,"body":"better? Right? How can we"},{"speaker":"Greg","startTime":2918.07,"endTime":2922.06,"body":"overcome these kinds of things?"},{"speaker":"Greg","startTime":2918.07,"endTime":2922.06,"body":"Whether it's, what if we don't"},{"speaker":"Greg","startTime":2922.06,"endTime":2925.21,"body":"have a super big sample size,"},{"speaker":"Greg","startTime":2922.06,"endTime":2925.21,"body":"even though we don't know what"},{"speaker":"Greg","startTime":2925.21,"endTime":2930.13,"body":"super big is? Or what if we"},{"speaker":"Greg","startTime":2925.21,"endTime":2930.13,"body":"don't have normality? Or? And"},{"speaker":"Greg","startTime":2930.13,"endTime":2933.16,"body":"this is really the tricky one."},{"speaker":"Greg","startTime":2930.13,"endTime":2933.16,"body":"What if we have mis"},{"speaker":"Greg","startTime":2933.16,"endTime":2936.49,"body":"specification in parts of what"},{"speaker":"Greg","startTime":2933.16,"endTime":2936.49,"body":"we're doing that the model isn't"},{"speaker":"Greg","startTime":2936.49,"endTime":2940.51,"body":"completely correct. So how do we"},{"speaker":"Greg","startTime":2936.49,"endTime":2940.51,"body":"rebound from those"},{"speaker":"Patrick","startTime":2940.78,"endTime":2941.86,"body":"vanilla ice cream?"},{"speaker":"Greg","startTime":2943.06,"endTime":2946.18,"body":"You know, about hang on a"},{"speaker":"Greg","startTime":2943.06,"endTime":2946.18,"body":"sec, whatever you're gonna say"},{"speaker":"Greg","startTime":2946.18,"endTime":2950.2,"body":"after this, it doesn't matter"},{"speaker":"Greg","startTime":2946.18,"endTime":2950.2,"body":"for this moment. You were coming"},{"speaker":"Greg","startTime":2950.2,"endTime":2954.31,"body":"up to my house, and I wanted"},{"speaker":"Greg","startTime":2950.2,"endTime":2954.31,"body":"everything to be nice for your"},{"speaker":"Greg","startTime":2954.31,"endTime":2959.26,"body":"visit. So I texted your daughter"},{"speaker":"Greg","startTime":2954.31,"endTime":2959.26,"body":"and asked her what kind of ice"},{"speaker":"Greg","startTime":2959.26,"endTime":2962.56,"body":"cream was it that your dad likes"},{"speaker":"Greg","startTime":2959.26,"endTime":2962.56,"body":"again? And she said, Well, he"},{"speaker":"Greg","startTime":2962.56,"endTime":2967.33,"body":"does like vanilla. But you could"},{"speaker":"Greg","startTime":2962.56,"endTime":2967.33,"body":"also surprise him with something"},{"speaker":"Greg","startTime":2967.33,"endTime":2971.89,"body":"like a pretzel caramel something"},{"speaker":"Greg","startTime":2967.33,"endTime":2971.89,"body":"so I'll be damned if I didn't go"},{"speaker":"Greg","startTime":2971.89,"endTime":2975.88,"body":"to like six different stores"},{"speaker":"Greg","startTime":2971.89,"endTime":2975.88,"body":"looking for this exotic ice"},{"speaker":"Greg","startTime":2975.88,"endTime":2979.3,"body":"cream to have in the freezer."},{"speaker":"Greg","startTime":2975.88,"endTime":2979.3,"body":"And when you came over and it"},{"speaker":"Greg","startTime":2979.3,"endTime":2981.64,"body":"was time for dessert, I opened"},{"speaker":"Greg","startTime":2979.3,"endTime":2981.64,"body":"up the freezer and I'm like,"},{"speaker":"Greg","startTime":2982.39,"endTime":2984.97,"body":"look at this and you're like oh,"},{"speaker":"Greg","startTime":2982.39,"endTime":2984.97,"body":"there's vanilla. That's all I"},{"speaker":"Greg","startTime":2984.97,"endTime":2991.57,"body":"need. Grab the vanilla. Pick."},{"speaker":"Greg","startTime":2984.97,"endTime":2991.57,"body":"Damn it. I went to six stores to"},{"speaker":"Greg","startTime":2991.57,"endTime":2992.53,"body":"find that for"},{"speaker":"Patrick","startTime":2993.82,"endTime":2998.86,"body":"the eyes remain styling"},{"speaker":"Patrick","startTime":2993.82,"endTime":2998.86,"body":"way in a bathroom. So that is"},{"speaker":"Patrick","startTime":2998.86,"endTime":3003.06,"body":"kind of my point. All right,"},{"speaker":"Patrick","startTime":2998.86,"endTime":3003.06,"body":"last week was least squares and"},{"speaker":"Patrick","startTime":3003.06,"endTime":3006.96,"body":"least squares as vanilla ice"},{"speaker":"Patrick","startTime":3003.06,"endTime":3006.96,"body":"cream. This week is maximum"},{"speaker":"Patrick","startTime":3006.96,"endTime":3009.81,"body":"likelihood. And what weirdo"},{"speaker":"Patrick","startTime":3006.96,"endTime":3009.81,"body":"flavor do you get? I think"},{"speaker":"Patrick","startTime":3009.81,"endTime":3013.98,"body":"Christie was just screwing with"},{"speaker":"Patrick","startTime":3009.81,"endTime":3013.98,"body":"the I don't. She's good. There's"},{"speaker":"Patrick","startTime":3013.98,"endTime":3018.54,"body":"very little in life that is more"},{"speaker":"Patrick","startTime":3013.98,"endTime":3018.54,"body":"fulfilling than a single scoop"},{"speaker":"Patrick","startTime":3018.54,"endTime":3020.58,"body":"of really good vanilla ice"},{"speaker":"Patrick","startTime":3018.54,"endTime":3020.58,"body":"cream."},{"speaker":"Greg","startTime":3020.669,"endTime":3022.559,"body":"All right, how's that"},{"speaker":"Greg","startTime":3020.669,"endTime":3022.559,"body":"gonna save us"},{"speaker":"Patrick","startTime":3022.589,"endTime":3025.859,"body":"ordinary least squares"},{"speaker":"Patrick","startTime":3022.589,"endTime":3025.859,"body":"was vanilla maximum likelihood"},{"speaker":"Patrick","startTime":3025.859,"endTime":3028.799,"body":"is that weirdo thing you bought"},{"speaker":"Patrick","startTime":3025.859,"endTime":3028.799,"body":"that will probably be there next"},{"speaker":"Patrick","startTime":3028.799,"endTime":3032.669,"body":"year, when I come up and visit."},{"speaker":"Patrick","startTime":3028.799,"endTime":3032.669,"body":"There's a time and a place for"},{"speaker":"Patrick","startTime":3032.669,"endTime":3036.059,"body":"that right is maximum likelihood"},{"speaker":"Patrick","startTime":3032.669,"endTime":3036.059,"body":"is a workhorse. And what we do"},{"speaker":"Patrick","startTime":3036.329,"endTime":3038.969,"body":"anyone out there who does"},{"speaker":"Patrick","startTime":3036.329,"endTime":3038.969,"body":"applied research, you've used"},{"speaker":"Patrick","startTime":3038.969,"endTime":3043.409,"body":"maximum likelihood, whether you"},{"speaker":"Patrick","startTime":3038.969,"endTime":3043.409,"body":"know it or not. But like"},{"speaker":"Patrick","startTime":3043.469,"endTime":3047.339,"body":"everything, at some point, the"},{"speaker":"Patrick","startTime":3043.469,"endTime":3047.339,"body":"bouncer is going to say enough."},{"speaker":"Patrick","startTime":3047.459,"endTime":3050.699,"body":"And he's going to grab you and"},{"speaker":"Patrick","startTime":3047.459,"endTime":3050.699,"body":"pull your arm behind your back,"},{"speaker":"Patrick","startTime":3050.729,"endTime":3053.729,"body":"which really, really hurts. And"},{"speaker":"Patrick","startTime":3050.729,"endTime":3053.729,"body":"then he grabs with his other"},{"speaker":"Patrick","startTime":3053.729,"endTime":3057.929,"body":"hand the color of your shirt,"},{"speaker":"Patrick","startTime":3053.729,"endTime":3057.929,"body":"and then drives you out. And if"},{"speaker":"Patrick","startTime":3057.929,"endTime":3061.529,"body":"you've been particularly"},{"speaker":"Patrick","startTime":3057.929,"endTime":3061.529,"body":"egregious, he opens the door"},{"speaker":"Patrick","startTime":3061.529,"endTime":3063.419,"body":"with your head. So"},{"speaker":"Greg","startTime":3064.14,"endTime":3067.29,"body":"that was a lot of"},{"speaker":"Greg","startTime":3064.14,"endTime":3067.29,"body":"familiarity and specificity."},{"speaker":"Greg","startTime":3068.7,"endTime":3069.39,"body":"Yeah,"},{"speaker":"Patrick","startTime":3069.93,"endTime":3074.91,"body":"I've got the mouth of a"},{"speaker":"Patrick","startTime":3069.93,"endTime":3074.91,"body":"280 pound weightlifter. And I"},{"speaker":"Patrick","startTime":3074.91,"endTime":3081.93,"body":"have the body of a 120 pound per"},{"speaker":"Patrick","startTime":3074.91,"endTime":3081.93,"body":"sale swim. Oops. So at some"},{"speaker":"Patrick","startTime":3081.93,"endTime":3086.7,"body":"point, the statistical bouncers"},{"speaker":"Patrick","startTime":3081.93,"endTime":3086.7,"body":"open the door with your head,"},{"speaker":"Patrick","startTime":3087.21,"endTime":3091.65,"body":"and you're gonna say I have a"},{"speaker":"Patrick","startTime":3087.21,"endTime":3091.65,"body":"modest sample size, I have"},{"speaker":"Patrick","startTime":3091.65,"endTime":3095.64,"body":"moderate non normality. I"},{"speaker":"Patrick","startTime":3091.65,"endTime":3095.64,"body":"absolutely know somewhere within"},{"speaker":"Patrick","startTime":3095.64,"endTime":3099.03,"body":"the confines of the model, I"},{"speaker":"Patrick","startTime":3095.64,"endTime":3099.03,"body":"have a mis specification. So not"},{"speaker":"Patrick","startTime":3099.03,"endTime":3102.36,"body":"only do these three things work"},{"speaker":"Patrick","startTime":3099.03,"endTime":3102.36,"body":"independently, but they work in"},{"speaker":"Patrick","startTime":3102.36,"endTime":3105.48,"body":"conjunction with one another."},{"speaker":"Patrick","startTime":3102.36,"endTime":3105.48,"body":"There are interactions between"},{"speaker":"Patrick","startTime":3105.48,"endTime":3108.51,"body":"all of these things. You're"},{"speaker":"Patrick","startTime":3105.48,"endTime":3108.51,"body":"rubbing your head, and you're"},{"speaker":"Patrick","startTime":3108.51,"endTime":3111.75,"body":"sitting on the bench out front"},{"speaker":"Patrick","startTime":3108.51,"endTime":3111.75,"body":"of the bar, and you're wishing"},{"speaker":"Patrick","startTime":3111.75,"endTime":3114.18,"body":"that you had picked up your cell"},{"speaker":"Patrick","startTime":3111.75,"endTime":3114.18,"body":"phone on the way out so that you"},{"speaker":"Patrick","startTime":3114.18,"endTime":3118.92,"body":"could get an Uber home. And you"},{"speaker":"Patrick","startTime":3114.18,"endTime":3118.92,"body":"say, you know why least squares"},{"speaker":"Patrick","startTime":3118.92,"endTime":3123.09,"body":"was pretty damn cool. And I"},{"speaker":"Patrick","startTime":3118.92,"endTime":3123.09,"body":"wonder if we couldn't reach past"},{"speaker":"Patrick","startTime":3123.09,"endTime":3127.47,"body":"your fancy pants ice cream, and"},{"speaker":"Patrick","startTime":3123.09,"endTime":3127.47,"body":"pull out what brought us to the"},{"speaker":"Patrick","startTime":3127.47,"endTime":3132.15,"body":"dance and see if we can't design"},{"speaker":"Patrick","startTime":3127.47,"endTime":3132.15,"body":"a version of that, that we can"},{"speaker":"Patrick","startTime":3132.15,"endTime":3137.37,"body":"apply in these situations. Who"},{"speaker":"Patrick","startTime":3132.15,"endTime":3137.37,"body":"do you know what's twice as good"},{"speaker":"Patrick","startTime":3137.49,"endTime":3142.11,"body":"as least squares to stage least"},{"speaker":"Patrick","startTime":3137.49,"endTime":3142.11,"body":"squares? Oh,"},{"speaker":"Greg","startTime":3142.35,"endTime":3143.37,"body":"double vanilla."},{"speaker":"Patrick","startTime":3146.13,"endTime":3147.48,"body":"That's what we'll talk"},{"speaker":"Patrick","startTime":3146.13,"endTime":3147.48,"body":"about next week."},{"speaker":"Greg","startTime":3147.51,"endTime":3150.93,"body":"I'm excited. I'm excited"},{"speaker":"Greg","startTime":3147.51,"endTime":3150.93,"body":"for least squares revenge."},{"speaker":"Patrick","startTime":3150.99,"endTime":3154.08,"body":"I love this stuff."},{"speaker":"Patrick","startTime":3150.99,"endTime":3154.08,"body":"We're going to post a couple of"},{"speaker":"Patrick","startTime":3154.08,"endTime":3157.83,"body":"citations on the show notes."},{"speaker":"Patrick","startTime":3154.08,"endTime":3157.83,"body":"There's some really good"},{"speaker":"Patrick","startTime":3157.83,"endTime":3162.36,"body":"tutorial resources on maximum"},{"speaker":"Patrick","startTime":3157.83,"endTime":3162.36,"body":"likelihood. netural Wasserman"},{"speaker":"Patrick","startTime":3162.36,"endTime":3167.16,"body":"Kutner has some wonderful stuff"},{"speaker":"Patrick","startTime":3162.36,"endTime":3167.16,"body":"in it. Ken Bolin in his 89 book"},{"speaker":"Patrick","startTime":3167.16,"endTime":3171.21,"body":"has a really nice exposition."},{"speaker":"Patrick","startTime":3167.16,"endTime":3171.21,"body":"That's a little more technical."},{"speaker":"Patrick","startTime":3171.21,"endTime":3176.58,"body":"It's not heavy. But if any of"},{"speaker":"Patrick","startTime":3171.21,"endTime":3176.58,"body":"you want a really approachable,"},{"speaker":"Patrick","startTime":3176.58,"endTime":3180.81,"body":"descriptive yet technically"},{"speaker":"Patrick","startTime":3176.58,"endTime":3180.81,"body":"proficient discussion of it, one"},{"speaker":"Patrick","startTime":3180.81,"endTime":3184.44,"body":"of my favorite is Craig Enders"},{"speaker":"Patrick","startTime":3180.81,"endTime":3184.44,"body":"has a textbook on applied"},{"speaker":"Patrick","startTime":3184.44,"endTime":3188.46,"body":"missing data. Totally. He has a"},{"speaker":"Patrick","startTime":3184.44,"endTime":3188.46,"body":"brand new edition now. Yeah, in"},{"speaker":"Patrick","startTime":3188.46,"endTime":3193.11,"body":"the first edition, chapter three"},{"speaker":"Patrick","startTime":3188.46,"endTime":3193.11,"body":"is one of the clearest"},{"speaker":"Patrick","startTime":3193.14,"endTime":3196.2,"body":"descriptions of maximum"},{"speaker":"Patrick","startTime":3193.14,"endTime":3196.2,"body":"likelihood estimation I've ever"},{"speaker":"Patrick","startTime":3196.2,"endTime":3199.05,"body":"seen. And so if you're"},{"speaker":"Patrick","startTime":3196.2,"endTime":3199.05,"body":"interested in this, or you're"},{"speaker":"Patrick","startTime":3199.05,"endTime":3202.32,"body":"looking to fold it into teaching"},{"speaker":"Patrick","startTime":3199.05,"endTime":3202.32,"body":"your own classes, that's a"},{"speaker":"Patrick","startTime":3202.32,"endTime":3203.58,"body":"really nice resource."},{"speaker":"Greg","startTime":3203.61,"endTime":3206.97,"body":"Totally agree. All right,"},{"speaker":"Greg","startTime":3203.61,"endTime":3206.97,"body":"well, so I am excited to talk"},{"speaker":"Greg","startTime":3206.97,"endTime":3209.76,"body":"about double vanilla next time."},{"speaker":"Greg","startTime":3206.97,"endTime":3209.76,"body":"Thanks, everybody. I hope it was"},{"speaker":"Greg","startTime":3209.76,"endTime":3212.43,"body":"useful for you to understand"},{"speaker":"Greg","startTime":3209.76,"endTime":3212.43,"body":"maximum likelihood a little bit"},{"speaker":"Greg","startTime":3212.43,"endTime":3214.83,"body":"better, which is something"},{"speaker":"Greg","startTime":3212.43,"endTime":3214.83,"body":"that's likely going on under the"},{"speaker":"Greg","startTime":3214.83,"endTime":3216.99,"body":"hood and the types of models"},{"speaker":"Greg","startTime":3214.83,"endTime":3216.99,"body":"that you run."},{"speaker":"Patrick","startTime":3217.05,"endTime":3220.56,"body":"And we both hope that"},{"speaker":"Patrick","startTime":3217.05,"endTime":3220.56,"body":"you achieved more by age 20 than"},{"speaker":"Patrick","startTime":3220.56,"endTime":3224.13,"body":"the two of us did put together."},{"speaker":"Patrick","startTime":3220.56,"endTime":3224.13,"body":"It's not hard really, it's not"},{"speaker":"Patrick","startTime":3224.13,"endTime":3231.93,"body":"hard. It has a low bar. Take"},{"speaker":"Patrick","startTime":3224.13,"endTime":3231.93,"body":"care everybody see ya. Thank you"},{"speaker":"Patrick","startTime":3231.93,"endTime":3235.02,"body":"so much for listening. You can"},{"speaker":"Patrick","startTime":3231.93,"endTime":3235.02,"body":"subscribe to quantity food on"},{"speaker":"Patrick","startTime":3235.02,"endTime":3238.2,"body":"Apple podcast, Spotify, or"},{"speaker":"Patrick","startTime":3235.02,"endTime":3238.2,"body":"wherever you download your"},{"speaker":"Patrick","startTime":3238.2,"endTime":3242.07,"body":"1980's heavy metal music to help"},{"speaker":"Patrick","startTime":3238.2,"endTime":3242.07,"body":"you relax and please leave us a"},{"speaker":"Patrick","startTime":3242.07,"endTime":3245.67,"body":"review. You can also follow us"},{"speaker":"Patrick","startTime":3242.07,"endTime":3245.67,"body":"on Twitter we are at quantity"},{"speaker":"Patrick","startTime":3245.67,"endTime":3249.39,"body":"food pod and check out our"},{"speaker":"Patrick","startTime":3245.67,"endTime":3249.39,"body":"webpage at quantity food pod.org"},{"speaker":"Patrick","startTime":3249.39,"endTime":3252.57,"body":"for past episodes, playlists,"},{"speaker":"Patrick","startTime":3249.39,"endTime":3252.57,"body":"show notes, transcripts and"},{"speaker":"Patrick","startTime":3252.57,"endTime":3256.71,"body":"other cool stuff. Finally, you"},{"speaker":"Patrick","startTime":3252.57,"endTime":3256.71,"body":"can join us at the d\u0026d lunch"},{"speaker":"Patrick","startTime":3256.71,"endTime":3260.1,"body":"table with your quantity and"},{"speaker":"Patrick","startTime":3256.71,"endTime":3260.1,"body":"theme merch at Red bubble.com"},{"speaker":"Patrick","startTime":3260.13,"endTime":3263.52,"body":"Where All proceeds go to Donors"},{"speaker":"Patrick","startTime":3260.13,"endTime":3263.52,"body":"Choose to support low income"},{"speaker":"Patrick","startTime":3263.52,"endTime":3268.08,"body":"schools, You have been listening"},{"speaker":"Patrick","startTime":3263.52,"endTime":3268.08,"body":"to quantum tude where we've told"},{"speaker":"Patrick","startTime":3268.08,"endTime":3270.84,"body":"every story and every joke we"},{"speaker":"Patrick","startTime":3268.08,"endTime":3270.84,"body":"know. So we're simply going to"},{"speaker":"Patrick","startTime":3270.84,"endTime":3273.99,"body":"start over at the top of the"},{"speaker":"Patrick","startTime":3270.84,"endTime":3273.99,"body":"list. quietude has been brought"},{"speaker":"Patrick","startTime":3273.99,"endTime":3277.56,"body":"to you by figuring out the new"},{"speaker":"Patrick","startTime":3273.99,"endTime":3277.56,"body":"post pandemic normal in"},{"speaker":"Patrick","startTime":3277.56,"endTime":3281.97,"body":"academia. Case in point. Today I"},{"speaker":"Patrick","startTime":3277.56,"endTime":3281.97,"body":"had my first faculty meeting for"},{"speaker":"Patrick","startTime":3281.97,"endTime":3285.39,"body":"the fall semester in which the"},{"speaker":"Patrick","startTime":3281.97,"endTime":3285.39,"body":"meeting was via zoom followed by"},{"speaker":"Patrick","startTime":3285.39,"endTime":3290.58,"body":"an in person reception. Oh,"},{"speaker":"Patrick","startTime":3285.39,"endTime":3290.58,"body":"okay, by a new organizing"},{"speaker":"Patrick","startTime":3290.58,"endTime":3294.0,"body":"framework for structural"},{"speaker":"Patrick","startTime":3290.58,"endTime":3294.0,"body":"equation models that subsumes"},{"speaker":"Patrick","startTime":3294.03,"endTime":3299.97,"body":"sem E, some D, some B some and M"},{"speaker":"Patrick","startTime":3294.03,"endTime":3299.97,"body":"some into the maximally general"},{"speaker":"Patrick","startTime":3300.0,"endTime":3306.33,"body":"WTF sound and by Twitter proudly"},{"speaker":"Patrick","startTime":3300.0,"endTime":3306.33,"body":"replacing two centuries of peer"},{"speaker":"Patrick","startTime":3306.33,"endTime":3312.36,"body":"review with a link to a preprint"},{"speaker":"Patrick","startTime":3306.33,"endTime":3312.36,"body":"This is most definitely not NPR"},{"speaker":"Patrick","startTime":3322.17,"endTime":3322.89,"body":"bom bom"}]}