Books like Thinking About Statistics — picked by fans

In the ongoing debates over artificial general intelligence (AGI), Judea Pearl is taking a firm stand: He argues that an intelligent robot should be able to reason about causality and that the currently fashionable approaches to AI miss this aspect.

A celebrated AI researcher and a Turing Prize laureate, Pearl has developed an amazingly original approach to this problem. This book is a high-end popular exposition of his approach.

But it’s so much more than that. It’s a history of statistics and its conflicted attitude to causality. It’s a story of heroes (or villains?) in this history. And it’s a scientific autobiography that describes Pearl’s journey. Pearl likes picking fights with the AI community, statisticians, or economists. He’s boastful, provocative, extremely intelligent, and knows how to tell a story.

As I write these lines, artificial intelligence (AI) is getting a lot of attention.

This is largely due to ChatGpt recently bursting onto the scene. But even before ChatGpt began making its mark, AI was often in the news. Some have expressed worry that it will take our jobs, others that it will reinforce systemic oppression by making racially or otherwise discriminatory decisions, and some have even voiced concerns that one day a superintelligent AI might pose an existential threat to humanity.

In the midst of all this, what might get lost is what AI is, what it's capable of doing, and what its limitations are. Wenger's book is intended to address all of these questions. It manages to do so in a way which goes into some of the mathematics of AI systems and yet remain accessible to a lay audience.

After laying out the technical aspects of AI,… show more.

Many quant geeks are familiar with statistics. The dominant school of statistical thought is called "Frequentist" or "Classical."

It focuses on either 1) testing a given hypothesis by determining how likely observed data are on the assumption that the hypothesis is true or 2) constructing intervals for which a certain percentage of them contain the actual value of whatever is being estimated.

A lesser known, although this seems to be changing, school of thought is Bayesian statistics. It focuses on using prior information about some phenomenon in order to revise or update one's beliefs about it.

If you're into stats but don't know much about Bayesian statistics, Donovan and Mickey's book is a great place to start. It's somewhat mathematical but covers the technical aspects much more accessibly that any other book I've seen on the topic. 

Many people associate mathematics with calculating things or plugging numbers into formulas to get answers to a multitude of problems.

But this isn't how mathematicians view their discipline. They see mathematics as more about starting with definitions of key mathematical concepts, stating axioms about these concepts, and proving things about them. For those interested in going from calculating and plug and chug mathematics to "real" mathematics, Richard Hammack's book is a terrific place to start.

The book covers a number of topics that cut across all of pure and applied mathematics, topics such as sets, relations, and functions. But the heart of the book is focused on how mathematicians go about proving things. If one wants a glimpse of how mathematicians really work, go out and get this book immediately.  

One of my favorite professors, Gretchen Martinet, used this to teach a course called “Mathematical Statistics” when I was at the University of Virginia. It is an extremely profound course full of dense but fundamental mathematical proofs in classical statistics. 

You will learn why the formula for the normal distribution is the way it is, why the sum of squares appears everywhere in statistics, and how to fit a linear regression by hand. In the same way calculus elevates our understanding of rates of changes, the book elevates your understanding of samples, averages, and distributions. Quant trading requires an intuitive sense of how data, models, and aggregates work, making this content essential for your success.

This book is kind of a fun crash course in statistics which covers all the basic concepts at an introductory level.

The cartoons are a little bit dated, but still entertaining. There are lots of pictures and graphs which are a pleasure if you are a visual learner. The reader will come away with many useful tools to help understand real world problems.

I’m a retired math professor, but still got a real kick out of this book and especially appreciated the many good examples referenced such as gender discrimination in salaries and racial discrimination in jury selection. I recommended it to many of my struggling students.

This book applies economic theory and econometric methods to problems in criminology.

It is divided into three parts. Part I discusses models of criminal recidivism. Part II describes the economic model of crime. Part III estimates cost functions for prisons.

Specific chapters cover statistical analysis of qualitative outcomes; analysis of two measures of criminal activity – the arrest rate and the conviction rate; and long-run estimates of cost functions for a group of Federal Correctional Institutions. 

I found a copy of this book in the sixties. That copy, much loved, was lost in moves and mayhem. Now, I only have a Dover reprint (water-logged during yet another move), but I have never been without and would search high and low if I were.

This is also a history of probability but with a very different focus. Ms. David was a statistician able to explain the calculations intuitively (good to assign to my students). But she was also thoroughly interested in the personalities involved. What was Galileo like? What happened to Pascal at Port-Royal?

I felt personally drawn into the historical narrative that often reads like a novel. 

All politicians should be forced to read this book. Anyone who reads a newspaper should be forced to read this book. My favourite radio programme in the world is Tim Harford’s More or Less. And this book is every bit as good. Harford is clear, incisive, and always interesting. In a world crowded with disinformation and fake news, he shows you how to evaluate the numbers that are thrown at you. To read him is to become a little cleverer. Make this man prime minister someone.

This provides a superb balance between technical aspects of R coding and the statistical methods that motivate its use. It's rare to find a book on topics like this that are written with Kabacoff's easygoing yet precise style, which makes it ideal for beginners. From my own experience, it is obvious the author has spent many years teaching this type of content, knowing where things deserve extra explanation up front and where other more technical details can be relegated to more advanced texts.