Ten Great Ideas about Chance

As the preface says, "this is a history book, a probability book, and a philosophy book". Many of the topics here are mentioned in easy reading popular science accounts of Probability, for instance  Chances Are . . .: Adventures in Probability . However the 10 chapters here are based on a 10 week Stanford course, and if one is paying Stanford tuition then one might expect more substance in a lecture course than can be found in easy reading popular science. And this book delivers.The stated Stanford prerequisite was one course in probability or statistics, which translates to "don't be afraid of mathematical notation". But this is not a standard STEM textbook explaining material at one particular level of sophistication. Instead, each 20-page chapter focusses on one topic, and is rather like listening to articulate experts explaining their subject and their own interests within that subject. So a chapter tends to start with simple ideas and then progress to verbal, or more mathematical, explanations of more sophisticated ideas.As the title says, these lectures are about Ideas, the history and content of the conceptual and logical foundations of probability and statistics. For the reader with such interests willing to put some effort, this book provides both a wonderful overview and a glimpse of some special topics. In other words, if the extract"If you were worried about where Bayes' priors come from, if you were worried about whether chances exist, you can forget your worries. De Finetti has replaced then with a symmetry condition on degrees of belief. This is, we think you will agree, a philosophically sensational result."appeals to you, then read this book. The reader interested in how probability and statistics are used today will likely prefer  The Signal and the Noise: Why So Many Predictions Fail-But Some Don't  or  Dicing with Death: Chance, Risk and Health .Disclaimer: I am friend and co-author of the first author. And I bought the book.

This is a tough, tough read, because the ideas are subtle and often very simple. But its worth it. Fundamental stuff, in the very strictest sense. Well written and thorough.

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 ;-)

Puts the entire development of humanity in a new perspective...

Sharpens your brain!

A book that will appeal to the maths and science geeks at first glance, considering ten of the past major breakthroughs that brought change to statistics and probabilities, yet something that can appeal to the curious, generalist reader too. These changes have been quite pivotal, having a very broad impact, and within the book the authors subject them to technical and philosophical scrutiny.To a non-mathematician this was a particularly fascinating topic to consider. The book brings to life many ‘everyday’ things, such as chance and probability – something that one takes for granted without knowing the back story or deeper implication. For a more involved specialist, they may form an entirely different connection, since the book manages to be attractive to both audience groups through its informed, accessible and engaging writing style. A few myths and misunderstandings may even be corrected along the way.This can be one of those books that you hadn’t considered you needed, but you will be glad you have read. It certainly can be a book that is hard to put down. If you are not particularly au fait with mathematics, some of the book may appear unfathomable, but fortunately the accompanying text can come to your aid and you can always skip a bit of the ‘deep maths stuff’ without affecting your enjoyment of the story-at-hand.Christmas is coming. This may deserve a space in a Christmas sack or two!

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.

El concepto de probabilidad es dificil, igualmente desde un punto de vista intuitivo y desde un punto de vista formal. Los diez apartados del libro ayudan enormemente a entender que es la probabilidad. El libro requiere conocimientos matematicos a nivel universitario.

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.

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.