Joseph Blitzstein: "The Soul of Statistics" | Harvard Thinks Big 4

professor Blitzstein is a professor of the practice of statistics he is known for teaching the popular class stat 110 introduction to probability which holds over 300 students each fall he also has over 200 thousand subscribers to the class on iTunes U his research interests focus on statistical inference for complex networks professor Blitzstein also enjoys chess and advises the Harvard chess club please join us in welcoming professor Blitzstein thank you all for coming thanks for introduction let's get started right away the title of my talk is the soul of Statistics let's start with with a motivating example before I tell you what I think the soul of statistics is so that Abraham Wald was a famous statistician and during World War two too many British bombers were being shot down by the Nazis so so he was consulting with them about Tron Tron trying to figure out where to put more armor you know they want to put more armor but the armors heavy and expensive they can't just put armor everywhere so where you put put the armor ok so I drew some airplanes here these don't really look like a bombers but that's ok so so so here's some airplanes and I just drew drew some bullet holes there there's one sorry I didn't have a warning that there would there be a graphic violence here so hopefully no one is too squeamish there's another one another one another one Bam Bam Bam Bam so these are just I just made up some some bullet holes on these planes and these are the planes that they get to observe there okay just as an example and so they brought in wall to ask you know where should they be put it putting more armor well the obvious thing to do is you know look at where all the planes are sustaining have heavy damage in our armor though those regions more however Walled said to do the exact opposite look for the parts of the planes where there isn't very little or no damage on the planes that that that came back the reason is so so for this example I protected that the nose on all of these planes and so what's really going on here well what we're really interested in is the planes that we didn't see those are the planes that that didn't come back the ones that you actually get to see are the planes that actually survived well enough to to to return so so there's there some statistical thinking in there how do you how do you learn about the planes you don't get to see and you know that requires some statistical assumptions and statistical thinking about what what do you do about the missing data right so maybe what if it looks like like this that did this plane we didn't get to see it because that's likely the Achilles heel or the Achilles nose of the plane and maybe there's like like a whole army of these like like Rudolph the red-nose or aircraft that we don't get to see any of them because they all died and we only saw the other ones so that's where you put the armor so so so so that that was your idea there's a pretty simple idea in retrospect but but easy to miss if you're not thinking statistically okay so that's an example of what's called selection bias in statistics what we know about what we get to see which is where the bullet holes are distributed for the planes that actually return but that's not what we're interested in we want to know about the planes that didn't make it back okay so how do we link those two things that that's a statistical problem now we're ready to say what the soul of statistics I won't keep you in suspense conditioning is the soul of statistics that means conditional probability for those of you know what that is if you don't know what conditional probability all it means is is that we're given information what we all we always have information wherever we're doing it's all conditional on the information that we have and conditional probability tells us how to update our beliefs based on information that we're able to observe every probability is conditional and so that that's the point of view here whenever you have a data set you want to think about how it was sampled so there's just a picture I'm not going to talk about of a network which is something I work on where a lot there's a huge amount of interest in networks these days but a lot of that work ignores where did the network come from how is it sampled and that can lead to very misleading answers if you ignore the sampling if you if you're not careful about what you're conditioning on and you know this is mostly Harvard thinks big so so I'm going to try to think really big that this is not just the soul of statistics this is everything because we wouldn't be if what I said was not true we wouldn't be here having this conversation it's all conditional on a huge conditional probability calculation that we can't actually do of things that that that brought us to the to this room to have this conversation right now everything is conditional okay so here's here's another example this is a longevity study from from 1835 Lombard was was interested in collecting huge amounts of data a very impressive data collection effort for how long people in different professions lived okay so I'll just give you a few of you I chose a few examples that that's a selection bias to the ones that I felt like choosing because because because it's a short talk so here's the profession here's the average longevity in his data set so it turned out that the first or second longest living people in his data set were chocolate makers so I was very happy to see that because I really like chocolate they lived to be seventy three point six which it you know lifespans have improved from 1835 to now so that's actually quite good back then and this is not second on the list but but one that I was interested in was professors lived to be 66.6 so I know it's a little bit sad you know I could have if I chosen a different career path I could have lived seven years longer and had all the chocolate that I want there is a sample size issue here which is he only had nine chocolate makers in his sample that's a bit very small sample there are a lot more professors than than chocolate makers in his study but anyway I want let's go on clock Smiths live to be fifty five point three so it's less attractive locksmiths 47.2 I was trying to figure out what why is there this discrepancy between clocks and myths and locksmiths so what could explain this I don't have an answer yet one more that is of interest to all of us his students unfortunately I have some bad news for up for all the students here in his study he found the average longevity of students was twenty point two years so I didn't want to be like get this event off to a depressing start I'm the first speaker and I don't want everyone to be too depressed to pay attention to the other talks that are coming up but twenty point two years you know it's worrisome I recommend that if you haven't seen Steve Jobs is a commencement address from Stanford 2005 I was there because because I was at Stanford it's a great talk Thanks and you know about living it each day to the max and and all that okay but there was an obvious problem with it with that logic right which is what are you conditioning on you know it's a student you know 20 years old is a normal age for a first for a student okay so it's kind of obvious to see what goes wrong it's a good example of looking at an extreme case because in the earlier profession it is not obvious that there all kinds of biases going on but when you see the simple and extreme case of a student you can see that the whole thing is very suspicious there's another issue I want to mention one more thing about that about censoring which is that we only know how long people lived after they died okay so usually it's a lot harder to talk to dead people than to talk to live people and professor Dench will be telling us about talking to dead people in detail but this is one case where it's much easier to deal with the dead people because we know how long they lived okay so there's a lot large amount of statistical survival analysis is a field to try a deal with the fact that we don't know how long the living people are going to continue to live and if we don't ever not careful about that we're going to get some bad bias all right one more example which is which is a very famous one in Dick's is regression towards the mean and it's it's everywhere so so just to take an example if you're not familiar with this take test scores so you have a group of students who take the SAT and then suppose that the ones who did really well take it again and the ones who did really poorly take it again so we're doing a selection okay well progression towards the mean says that we expect the one the students who did really well on the SAT when they retake it their scores are going to tend to go down towards the mean ones who did really poorly are going to go up there's examples everywhere one of the first examples I'm not going to go through this data table here but that that's just for historical curiosity Sir Francis Galton who is a cousin of Darwin was one of the first or possibly the first person to clearly explain regression towards the mean and he discovered it by studying Heights parents and children's heights and he found that for example if you look at fathers and sons so we don't have to work worried about differences gender differences in Heights let's just take fathers and sons okay so he looked at very tall fathers how tall are their sons well the sons are still pretty tall but they were regressing towards the mean okay and very short fathers their sons tend to be taller not not all the way to the mean this is regression toward the mean not to the mean but it's moving in that direction that phenomenon is everywhere in statistics and in life so if you have your eyes open to look for it that's a good thing and so I just want to quickly quote Daniel Kahneman because it's a beautiful quote about regression towards the mean he said I had the most satisfying Eureka experience of my career while attempting to teach flight instructors that praise is more effective than punishment for promoting skill learning and when he gave that talk a flight instructor objected on many occasions I've praised flight cadets for clean execution of some aerobatic maneuver and in general when they try it again they do worse on the other hand I've often screamed at cadets for bad execution and then they do better the next time so don't tell me that reinforcement works and punishment does not incontinence that's a joyous moment because he what he what he realized is we tend to reward others when they do well and punish them when they do badly and because there's regression to the mean he should say toward the mean it is part of the human condition that we are statistically punished for rewarding others and rewarded for punishing them and so there are a lot of misconceptions about regression toward the mean that that I don't have time to get into detail of but I want to get do a quick little picture illustrating a hypothetical thought experiment what would the world be like without regression toward the mean because a lot of people seem to have the misconception that regression toward the mean would mean that everyone is going to be you know eventually converging to the to the same value and actually without regression toward the mean well we need regression toward the mean in order to have stability in the population so I just made up a simple example where suppose we had three people three different heights and suppose each person has a child who's equally likely to be a little bit shorter the same height or a little bit taller okay so I just gave them three three kids each a little shorter same height a little bit taller so that's the next generation then I just took that generation just just rearranged that these are the same people now same thing happens again that's the next generation and then I'll just take one more generation this is this is what the population would look like without regression toward the mean well you see is after only three or four generations you know you're going to see giant you know ten-foot people walking around and you have little four-inch feet people things like that that's what the world would be like without regression toward the mean okay lastly I want to tie this bet back to this kind of personal perspective on teaching and research which is something I call the conditional golden rule but this was a course evaluation I got on the cue guide a few years ago so so someone wrote it was a clap this is about stat 110 it was a class that was designed by blitz with the Credo I wanted to teach a class that I would want to take myself so I was really happy when I saw that because I compose a nice comment but it also reminded me of something that I had for on that I had said and I kind of liked I liked that however in the interest of full disclosure that same year there was also a comment that said writes horrible problem sets that only caused pain not learning so unfortunately I try to be logical the logical conclusion from these two things is that I'm a masochist so let me just so let me just tell you what the conditional Golden Rule is and then I'll stop that this is my philosophy of teaching in a nutshell do unto others as you would have do unto you except it's conditional right everything is conditional it's the class that I would take conditionally on having the same interest and background and knowledge so I just try to do the conditional golden rule and trying to follow it right now and giving this talk and if I failed blame the conditional golden rule or blame or blame the fact that conditional probability is hard as we see in stat 110 it's hard but but it's worth thinking about okay so I just want to thank the organizers and thank my colleagues especially carl morris shelly mung and dave harrington and all my stat 110 students in TFS and all of you for coming thank you

Channel: Harvard University

Views: 100,353

Rating: 4.953434 out of 5

Keywords: joseph blitzstein, joe blitzstein, statistics, stats, harvard thinks big

Id: dzFf3r1yph8

Length: 14min 47sec (887 seconds)

Published: Thu Feb 28 2013