The best books on statistics from a statistician

David J. Hand Author Of The Improbability Principle: Why Coincidences, Miracles, and Rare Events Happen Every Day
By David J. Hand

Who am I?

When people ask me why I became a statistician, and what its attraction is, I simply tell them that, using statistics, I have been on voyages of discovery and travelled to worlds they didn’t know existed. Using data and statistical methods instead of light and optics, I have seen things others could not imagine. Like an explorer of old, I have joined adventures peeling back the mysteries of the world around us. In my books on statistics, data science, data mining, and artificial intelligence, I have tried to convey some of this excitement, and to show the reader how they too can take part in this wonderful modern adventure.

I wrote...

The Improbability Principle: Why Coincidences, Miracles, and Rare Events Happen Every Day

By David J. Hand,

Book cover of The Improbability Principle: Why Coincidences, Miracles, and Rare Events Happen Every Day

What is my book about?

Coincidences happen, incredibly unlikely things occur, and the apparently miraculous comes about. The improbability principle says that extraordinarily improbable events are commonplace. It shows that this is not a contradiction, but that we should expect identical lottery numbers to come up, lightning to strike twice, to meet strangers with your name, financial crashes to occur, and ESP experiments to produce positive results.

The book shows how all of these, and more, are straightforward consequences of the five solid mathematical laws constituting the improbability principle: the law of inevitability, the law of truly large numbers, the law of selection, the law of the probability lever, and the law of near enough.

The books I picked & why

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Principles of Statistical Inference

By D.R. Cox,

Book cover of Principles of Statistical Inference

Why this book?

This is a deep and beautifully elegant overview of the ideas underlying statistical inference. It is the finest concise outline I know of the foundations, dealing with the key concepts and ideas in an accessible way. Written by one of the leading creators of modern statistics, without unnecessary mathematics or superfluous detail it includes a balanced description of the fundamentals of distinct schools of thought, such as Bayesian and frequentist schools. The book did not exist when I started learning statistics, but I am certain I would have understood the discipline’s subtleties much sooner if it had.

Computer Age Statistical Inference, Algorithms, Evidence, and Data Science

By Bradley Efron, Trevor Hastie,

Book cover of Computer Age Statistical Inference, Algorithms, Evidence, and Data Science

Why this book?

If you want to find out how to make discoveries using modern data science tools, this is the book to read. My career has been based on developing and applying statistical tools. The infrastructure underlying these tools is the computer – the computer and I grew up in parallel. And it is no exaggeration to say that the computer has revolutionised the practice of statistical analysis, replacing the tedium of manual arithmetic with powerful instruments for probing and examining data sets.

On the one hand, computers allow us to store and manipulate vast data sets, while on the other hand, they have opened up entirely new vistas, allowing us to apply tools that would have been impossibly time-consuming for previous generations to use. In this way, we can probe the world in completely novel ways, and this underpins the data science, machine learning, and artificial revolution we are now witnessing.

This book describes those tools, where they come from, and how they shed insight into the world about us. It puts them in a historical context and illustrates important modern applications. It is also one of the most beautifully produced books in my library.

The Elements of Statistical Learning: Data Mining, Inference, and Prediction

By Trevor Hastie, Robert Tibshirani, Jerome Friedman

Book cover of The Elements of Statistical Learning: Data Mining, Inference, and Prediction

Why this book?

I’ve written 31 books on statistics, machine learning, AI, and related areas. But I wish I’d written this one. It’s a superb outline of modern statistical learning theory, encompassing cutting-edge statistical and machine learning methods. I have found it immensely valuable as a source of clear descriptions of the range of modern tools, including methods such as neural networks, ensemble methods, support vector machines, and putting them into context. Liberally illustrated with examples, it enables the reader to see how and why the methods work, and what sort of questions can be answered by the different methods. 

An Introduction to Probability Theory and Its Applications, Vol. 1

By William Feller,

Book cover of An Introduction to Probability Theory and Its Applications, Vol. 1

Why this book?

This is my go-to book for when I need to find proofs or examples of the theory or applications of probability. It’s an old book now, but it remains unsurpassed as an outline of the foundations of classical probability theory. The preface to the second edition says “in addition to an unexpected number of users, the book seems to have found friends who read it merely for fun; it is most heartening that they range from pure mathematicians to pure amateurs”. And that must surely be exactly right: I find myself re-reading it because of the insights and perspectives it sheds. 

Kendall's Advanced Theory of Statistics, Distribution Theory

By Alan Stuart, Keith Ord,

Book cover of Kendall's Advanced Theory of Statistics, Distribution Theory

Why this book?

This is a wonderful book because it says it all. Of course, that’s an exaggeration because no book could possibly encompass the vast breadth of modern statistics, but anyone who read through this multi-volume work would have an enviable knowledge of the discipline. It’s an unsurpassed general source of information about the foundational concepts and tools of statistics, and a reference source I regularly turn to when I need to remind myself of the theory underlying a concept or method.

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