NB. I was sent this book as a review copy.

This book straddles a tricky middle ground, given that it introduces topics from scratch and goes into some very specific details of them in a relatively few pages, before jumping onto the next. On starting to read it, I was skeptical of how this could possible work, but by the end of it I believe that I saw the real utility of a book like this. The audience is quite specific, but for them it will be a gem.

The book covers a huge range of ideas related to chance, from the underlying mathematics of probability, to the psychology of decision making, the physics of chaos and quantum mechanics, the problems inherent in induction and inference and much more besides.

The book is taken from a long-running course at Stanford which the authors taught for a number of years, and they have tried to condense down the most important aspects of it to a relatively light book. At 200 pages, a great deal is packed into this, and as such, anyone without a good foundation in mathematics will certainly find a great deal of it too advanced. As I was reading it however, I realised that a first or second year mathematics or physics student (or even more advanced), taking a course in statistics would find this a perfect addition to their course notes or prescribed text book.

The book covers the history of ideas which have shaped our understanding of chance, stretching back millennia, and including research which is ongoing, as well as contentious, and as such will beautifully contextualise what is learned in a lecture course which is unlikely to give quite the grounding that this book gives. The biographical and historical insight from economists, philosophers, psychologists, mathematicians and physicists, amongst other people, will give a far better framework to the ideas which in my experience helps to give a deeper understanding of how everything fits together.

And perhaps that is really the idea of this book. Though the chapters are not specifically contiguous, it really is a book about how these very disparate topics fit together, often in surprising ways, historically as well as mathematically.

If I have a slight criticism of the book it is that in a few places, ideas are introduced in slightly awkward ways, and then used without giving quite the understanding necessary to follow the details. If used in conjunction with a course which covers similar topics however, this will not be a problem. The clearest example of this for me was in one of the first chapters, where the idea of a Dutch Book is introduced, without quite explicitly stating what it is…. though perhaps this is my own lack of knowledge showing through. In the same chapter, some of the mathematical writing is slightly sloppy, but as this is not a text book, this can also be forgiven.

All in all, I would recommend this to any student studying or having studied anything statistics related at university, if only to give a much wider perspective than would be given in a course. It is so often useful to have both the forest and the trees, and this provides precisely the map of the interlinking forests which would certainly have been very satisfying for me as an undergraduate student first coming across these ideas.

Book reviews – MathemafricaMarch 18, 2018 at 1:18 pm[…] Ten Great Ideas about Chance – By Persi Diaconis & Brian Skyrms, a review […]