Favorite Stats Books: Seven Pillars of Statistical Wisdom

Key Takeaways

hello everybody welcome back to a new video in this video we'll be talking about a new one of my favorite books it is the seven pillars of statistical wisdom why statistics because my introduction to statistics in let's say recent years so i studied a little bit of statistics when i was doing my computer science degree but the more i went into machine learning and ai you start to have to deal with a lot of statistical concepts because a lot of machine learning i mean statistics is one of the let's say two or three foundations of machine learning next to computer science and mathematics and when you learn about these statistical ideas in the let's say in your journey to learn machine learning a book like this is very interesting because it pulls out these threads of statistical ideas um and it puts them into historical context it's a very accessible book we'll go into exactly the seven ideas but what the book does is to say these are seven major ideas of statistics that are foundational to the statistics as we know it today and then built on top of these seven is a lot of other statistical ideas but also machine learning and ai sort of come on top of this structure of statistics i love this book because it's very accessible it's easy to pick up and learn and read it's not explaining the ideas in sort of mathematical ways it's it's a really smooth way of storytelling the origins of these ideas how they developed the people around them and the kinds of problems that they were trying to solve when they came up with these let's say revolutionary methods so as somebody who's maybe didn't have the best time with the statistics textbooks uh back in school because they went right into uh you know when you toss a coin 100 times or a thousand times what happens and that's a very important and sort of rigorous understanding of statistics uh but this is a very sort of human look at looking at the history of those ideas those main extremely important and that you can maybe take for granted now if you don't see them in the proper historic light that this book puts them in so let's get into the seven pillars of statistical wisdom and see what those seven are so this is the seven pillars of statistical wisdom by stephen stiegler it's a very small book and it's very easy to go about there are a bunch of visuals on there highly really good sort of storytelling style off of the book but then what are the seven so the seven ideas or the seven pillars that a lot of modern statistics is built on top of one is aggregation from tables and means to least squares information its measure and rate of change likelihood calibration on a probability scale intercomparison within sample variation as a standard regression so multivariate analysis bayesian inference and causal inference design experimental planning and the role of randomization and residual scientific logic model comparison and diagnostic display now for me i would say the three that i sort of most enjoyed were aggregation information i really want to spend a bunch more time on likelihood but regression was also extremely important so aggregation is basically the idea that you can gain more information sometimes by throwing away information that you have so let's say an average if you have 100 measurements you can average them to have only one number and that number tells you something that maybe the hundred don't tell you and with that you can gain more information the intro [Music] chapter explains these in in a very good way aggregation is the combination of ideas so you gain you can gain information by throwing information away and that is sort of revolutionary the second pillar is information so information measurement and that's the idea that if you have 20 measurements of let's say a phenomena and then you have you go out and take 20 more measurements you're not doubling the information that you have the first 20 actually gave you more information than the second 20 and that's the square root of the number n of observations likelihood is the calibration of inference with the use of probability intercomparison which is the idea that you can gain some insight by comparing a data set to itself intercomparison is the fourth pillar the fifth is regression and the idea here is to get from galton's uh ideas about regression to the mean and how that sort of explains some of the questions raised by darwin's theory of evolution and from regression to the mean you have concepts like regression in prediction so the work in fact introduces modern multivariate analysis design of experiments is the sixth pillar and then the seventh is residuals to paraphrase these seven ideas the author puts these lists which is what is the value of targeted reduction or compression of data so that's aggregation the diminished value of an increased amount of data so your first 20 is maybe has more information than your second 20. how to put a probability measuring stick to what we do that is likelihood how to use internal variation in the data to help in that how asking questions from different perspectives can lead to revealingly different answers that would be regression and then the essential role of the planning of observations so how you design experiments and the importance of being careful in that and how all these ideas can be used in exploring and comparing competing explanations in science so this has been a quick look to the seven pillars of statistical wisdom very readable uh intro to very interesting and important statistical ideas highly recommended i've been going over it and i plan to spend even more time with it curious to see what you think about it let me know in the comments below thank you for watching