The most recommended probability books

We are primed to measure things against the yardstick of averages, judged according to how closely we come to it or how far we deviate from it. It affects our own self-confidence, how we view and grade our performance and worth.

The assumption that metrics comparing us to an average--like GPAs, personality test results, and performance review ratings--reveal something meaningful about our potential is so ingrained in our consciousness that we don't even question it. That assumption is spectacularly—and scientifically—wrong. 

Together with great stories about the folly of averages (the one about pilot chairs really got me) and many research facts and stats it conveys a very important message about how we view the world.

I really liked Williams’ writing style. He is very clear, provides good examples, and is very careful in his argumentation.

I very much liked – and indeed borrowed – his strategy of summarizing the main arguments of each chapter. This is especially important since his book addresses a wide range of challenges in social science. I especially liked his discussion of how the variables we measure are never perfect proxies for the phenomena that we hope to understand.

I also liked his careful discussion of how social scientists need to be more reflective in their work. And I found his discussion of the nature of causation in social science deeply insightful.

One day, in conversation with Ian Hacking, he announced a new passion: Archaeology of ideas. The concept we now have of probability was new, he said; it was born in the 17th century and was different from anything before!

I love this book because it is, first of all, a philosopher’s take on history. Hacking confronts the conceptual puzzles that defeated some of the best mathematical minds, raises controversial questions about what it all meant, and gives us a new vision of the history of concepts.

What could be more exciting?

When people think of financial planning, their first thought is investing. Their second thought is retirement.

Kaplans explain risk succinctly: “Everything is possible, yet only one thing happens.” People understand risk but don’t really understand how to apply it rationally to investing (market risks) or to retirement (longevity risk).

But first, having an understanding of what risk is and isn’t, and where it comes from is important before you can apply it to what fuels your plans – markets and longevity.

This book helped me formulate the basic planning concepts I use in my book since personal finance is all about taking risks – as are any other decisions and actions you take in life.

This was the book that set me on the path to becoming a Reliability Engineering specialist. (Reliability Engineering being a subset of Mechanical Engineering). This book was my first exposure to reliability engineering lore, covering subjects such as the Weibull Distribution and the probabilistic approach to engineering reliability. To design and manufacture an engineering system is one thing – how to make it reliable enough to last for its projected lifetime is another. More emphasis is now being placed on these aspects of the engineering life cycle – the operation, maintenance, and divestment phases. This approach has sometimes delivered systems an order of magnitude more reliable than their 20th Century forebears.

You can always rely on a children’s book published by Usborne, the Big Maze Book by Kirsten Robson is no exception. It offers 50 different mazes to solve, each charmingly illustrated. The mazes themselves are nice and varied, incorporating different settings, different subject matter, and slightly different visual treatments, which all helps to keep solvers interested. As a whole, this book would probably appeal more to younger children who still enjoy picture books. That being said, the mazes do get progressively harder through the book, so there is something there for the slightly older ones too.

This ambitious book, written by a distinguished philosopher, is a contribution to what might be called the “epistemology of evolutionary biology.” Sober starts by offering a general analysis of the concept of evidence based on probability theory, then applies this analysis to issues in the theory of evolution. He explains why the evidence favours evolution over the hypothesis of “intelligent design,” then tackles the thorny methodological problem of how to infer evolutionary history from observations on contemporary species. Though difficult, the book is clearly written and repays close study.

My knees tremble and my heart quakes when I think of how much work must have gone into these two companion volumes. Collectively, they are more than four times the length of my book, covering the whole of machine learning.

It is an essential encyclopedic resource that should be on the desk of anyone serious about machine learning.

Sadly, Games, Gods, and Gambling by FN David is out of print. This is the next best thing. Lorraine Daston has the supreme gift of making the complicated idea seem straightforward. This is an account of the frenzy for measuring that happened in the 18th century, and how it made the world we live in today, when the gambler’s eye for odds has become the algorithm of taming chance that guides all our decisions.

An authoritative tome on R. This book is the ultimate reference guide, heavy on statistical methods from the simple to the advanced. Of the 29 chapters, only the first five chapters or so have R syntactical and programming skills as their main focus; the remaining content highlights the many and varied statistical techniques R is capable of. I think this is a fantastic book to have on the shelf for people who are likely to need R and its contributed packages for a variety of different statistical analyses, but might not know where to initially start for any given statistical method.