Probability for Statisticians

This the the second edition of the book, and is significantly streamlined when compared to the first.

It discusses measure theoretic probability from the viewpoint of what a theoretical statistician needs to know, and includes many details that an applied statistician may need to look up on occasion. For that purpose I think the book is very well suited but I hadn’t already had a course at the level of Billingsley’s Probability and Measure I think I would have found it hard going.

Reading it frequently feels like you are sitting next to the author, with him pointing out the important parts, and suggesting how to think about things. I enjoyed that aspect very much, and it helps to solidify the readers understanding.

The topics cover all the standard measure theoretic probability stuff you need, and many more statistical topics are developed in some depth: bootstrapping, Winsorization, Essen bounds, Edgeworth expansions, etc. and for my money, the nicest introduction to empirical processes around.

If you have the background, interest, and need, see publisher’s web page for the table of contents, preface and chapter 2 on “Measurable Functions and Convergence.”

Peter Rabinovitch is the head of Data Science at ZetaTango Technology. He has been doing data science since long before “data science” was a thing.