The best probability books

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.

These are volatile and tumultuous times, which makes it difficult if not impossible to make decisions with any assurance of accuracy. Kay and King, in this very substantial and learned book, have written what we think is one of the best guides to making these decisions with the best tools and insights we have. The authors have the advantage of being very seasoned practitioners in several domains as well as extremely well-read in the subjects that impact decision-making under these conditions. Their emphasis is on the limits of current mathematical tools, and they advise that we use the more pragmatic and grounded understanding we have from history, philosophy, and our own experiences.

A few years ago at my son’s annual townhall in school, the principal outlined the school’s strategic game plan on a powerpoint presentation.

One of the slides that stayed with me projected a visual from the book The End of Average: How We Succeed in a World That Values Sameness.

I went back and read the book, only to realize that it resonated deeply with how we in the corporate world today (not just in schools at the elementary, middle, or senior levels) are quick to pronounce verdicts: below average, average, exceeds expectations.

The book poses some pertinent questions, and rightly so: Who came up with this principle of average? Why are we following it everywhere?

How often have we as managers just given up on people that we perceive are not ‘leadership’ material. Often these same average or poor performers can be great performers in different contexts.

Todd Rose… show more.

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.

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.

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.

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.

The previous book is about the most prevalent forms of AI, many of which focus on prediction or classification.

For example, a bank may use an AI system that utilizes data about those applying for a loan to predict whether they're likely to default. The judicial system might use an AI model which takes into account a convicted person's attributes in order to predict whether that person is likely to re-offend. A hospital might observe attributes of cells in order to classify them as cancerous or not.

Judea Pearl, a computer scientist at UCLA, has been in a long-running effort to get those working in AI to focus more on designing systems which could engage in causal reasoning. And in doing so, he's had a major influence on a number of disciplines, including computer science, philosophy, statistics, epidemiology, and the social sciences.

In The Book of Why, Pearl teams up… show more.

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.

Everyone knows what probability is, and we all understand how a coin flip works, but not everyone can explain the optimal betting strategies for a roulette table. We don’t study probability to understand the likelihood of events. We study probability to understand the expected outcomes of business processes that depend on those events.

In other words, this book won’t just teach you about probabilities, it will teach you about business strategies associated with those probabilities. It will help you answer a question like: How do I maximize the profit on this life insurance policy, given this set of survival probabilities? It isn’t just a likelihood question, it is a business question. I highly recommend that anyone studying probability does so through an actuarial lens.

This is a more comprehensive and mathematically rigorous book than Pierce’s book. For the novice, it should be read-only after first reading Pierce’s more informal text. Due to its vintage, the layout is fairly cramped, but the content is impeccable. At almost 500 pages, it covers a huge amount of material. This was my main reference book on information theory for many years, but it now sits alongside more recent texts, like MacKay’s book (see below). It is also published by Dover, so it is reasonably priced.

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.