Ten Great Ideas about Chance by Persi Diaconis (PDF)

Description

A fascinating account of the breakthrough ideas that transformed probability and statisticsIn the sixteenth and seventeenth centuries, gamblers and mathematicians transformed the idea of chance from a mystery into the discipline of probability, setting the stage for a series of breakthroughs that enabled or transformed innumerable fields, from gambling, mathematics, statistics, economics, and finance to physics and computer science. This book tells the story of ten great ideas about chance and the thinkers who developed them, tracing the philosophical implications of these ideas as well as their mathematical impact.Persi Diaconis and Brian Skyrms begin with Gerolamo Cardano, a sixteenth-century physician, mathematician, and professional gambler who helped develop the idea that chance actually can be measured. They describe how later thinkers showed how the judgment of chance also can be measured, how frequency is related to chance, and how chance, judgment, and frequency could be unified. Diaconis and Skyrms explain how Thomas Bayes laid the foundation of modern statistics, and they explore David Hume’s problem of induction, Andrey Kolmogorov’s general mathematical framework for probability, the application of computability to chance, and why chance is essential to modern physics. A final idea—that we are psychologically predisposed to error when judging chance—is taken up through the work of Daniel Kahneman and Amos Tversky.Complete with a brief probability refresher, Ten Great Ideas about Chance is certain to be a hit with anyone who wants to understand the secrets of probability and how they were discovered.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I probably set myself up for a fall with this one.For starters, I’m a big fan of Persi Diaconis. Not only is he Greek, not only did he teach Math at my alma mater, but he’s a proper, self-taught genius. And he’s modest. Not once in the book does he mention that he’s the man who proved mathematically that a deck is random once you’ve shuffled seven times.Also, I’m a big big sucker for Probability, which I studied a fair bit both as an undergrad and as a graduate student. Indeed, if you go to amazon.co.uk you’ll see I have the definitive review (with errata and corrections to the homework problem solutions) for Capinski and Kopp’s “Measure, Integral and Probability.”And I’m an even bigger sucker for popular science and popular math. I devour popular science books whole, most recently Roger Penrose’s “Faith, Fashion and Fantasy” (no idea what that was all about, but it blew me away anyway) and Carlo Rovelli’s “Seven Brief Lessons in Physics,” which fooled me into thinking I understand General Relativity.On pages 115-116 the authors even dedicate a chapter to the work of a former role model of mine, my high school’s 1984 Valedictorian, John Ioannides! I still remember sitting in the audience as he was delivering his speech. It felt great to read about him in a book by Persi Diaconis.So I’m devastated to report that this is an underwhelming book.Don’t get me wrong:• the topics are expertly selected• the style is friendly• a story is told• there is a beginning and an end• you are left in no doubt of the beauty of the subject• the references are all there if you want to study the topics on your own• the authors’ love of Math is evidentHowever, and this is an enormous problem, if there is an idea you did not understand before, you are extremely unlikely to get to terms with it by dint of having read this book. Indeed, there’s stuff I have in my life been an expert on that I read here and I was not able to recall it.The chapters are invariably a mix of1. a trivial example that does not penetrate enough the intended topic because it contains too much of the familiar and too little of the topic that’s being introduced2. references to original texts that are nineteenth century translations into stilted English from eighteenth century originals written in French or German or Latin3. statements of complex results that would take fifty pages to arrive at if the proofs were shown4. cheerleadingSo what I re-lived by reading this book is my Freshman Year nightmare Math class where three times a week I’d follow the first five minutes of the lecture only to subsequently find myself furiously copying from the board so I can read my lecture notes later at home and try to make sense of them.And I got to remember the worst part of that package, which was that sometimes the teacher would make a mistake on the board, which of course would cost me hours of private desperation as I tried to see how that was compatible with everything else I’d copied down.Not saying there are mistakes in the main body of the book, but perhaps there are, because there’s at least a couple of absolute HOWLERS in the “probability tutorial” in the back.I’ll tell you one thing: the poor souls at Stanford who took this class as a distributional requirement learned absolutely nothing. That I promise you.Bottom line, after reading Rovelli I feel comfortable lecturing my mom on General Relativity, a topic I know nothing about. After reading this book I’m afraid to discuss Probability even with my colleagues at the startup I’m running. Dunno, perhaps I’m merely “confused about higher things.”All that said, this was the guided tour to the brain of a genius. Three-and-a-half stars from me 😉

⭐Nobody I know is better placed to write about probability than Persi Diaconis, and Brian Skryms appears to be his equal as a philosopher. Beginning with equiprobable cases in games where symmetry is built in so that equiprobability is the natural basis for analysis, Diaconis and Skryms build to more complex and less obviously symmetric situations, showing the power of Reverend Bayes’s methods.Every sort of delicate difficulty with the notion of randomness is considered, culminating with the conclusion that there are sequences of numbers that pass every test for randomness. That is, sequences against no scheme of betting can be assured a win. No “Dutch book” against them is possible. However, there is no way to exhibit even one such sequence. Their existence is assured only by invoking the Axion of Choice. This principle says, in effect, that if a set of conditions is not self-contradictory, then there must exist a think satisfying those conditions.The idea that every conceivable event can be assigned a probability in a consistent way seems a stretch. The idea that in everyday life this can and should be done so that we may better guide out lives, seems even less probable. And it is clear that people do not live their lives this way, except with regard to special sorts of things, where they circumstances are regular enough that assignment of probabilities is eminently sensible, and where the gains from using a quantitative approach are sufficient to justify their costs. So I wish that Persi and his co-author had said more about the circumstances in which it is most appropriate to think quantitatively and apply Baysean analysis.As an example, Persi told me that he undertook the experiments and analysis he, Susan Holmes, and Richard Montgomery undertook of coin flipping in part because of a few “loaded” coins I sent him as a joke. These suggested looking into the dynamics of coin-flipping. If you look at their joint paper, you will see that a lot of physical experimentation and careful analysis went into it. So they thought it was worth it to work out, theoretically and experimentally what was going on – the probabilities and dynamics. But previously no one had done this. Likewise you may be certain that the probabilities and dynamics of many common processes are yet to be known and understood. For instance, what is the probability that someone with your general characteristics will develop pancreatic cancer? There are numbers out there, but how well do they reflect the probabilities for people closer and closer to you in characteristics. And how accurate or complete is the data on which these numbers are based? You don’t know, nor does anyone else.So what sorts of things have probabilities that can and should be worked out? I would like to know what Persi Diaconis and Richard Skryms have to tell us about this. Nothing definitive can be said, but that are wiser that almost anyone else.A great, interesting, and challenging book. Buy it or borrow it and see what you can learn form it.

⭐As a non-mathematician, I went straight to the probability tutorial in the appendix, as recommended by the authors. I found a howling, elementary error in the math there, which I must confess has somewhat dented my trust in the reliability of the book. It’s the opposite of a systematic survey, but I very much like the historical approach to discussing problems in probability and I’ve been enjoying it so far.

⭐There are nuggets of real interest in here but too often the book jumps from a difficult to understand (because of the way it was written) original text of several centuries ago to a sketch proof which manages to be both too compressed and too complex at once.

⭐The erudition exhibited in this book is unparalleled. Tackles important questions with insight and depth, whilst being an enjoyable read. The many historical references are fun and give background and context to better understand the development of ideas

⭐Beautifully written with wonderful mathematics included.

⭐A wonderful resource I wish I had read years ago. Summarized the important history of statistics, and more importantly the problem of induction in a clear digestible way.Unfortunately the kindle is not a properly formatted ePub making reading the endnotes a painful and frustrating exercise.

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