Essentials of Probability Theory for statisticians

A textbook that provides graduate students with a rigorous treatment of probability theory, with an emphasis on results central to theoretical statistics. A classic measure-theoretic approach is presented and motivated by examples in biostatistics, such as outlier tests, monitoring clinical trials, and adaptive clinical trial design changes based on accumulating data. Different methods of proofs their usefulness for establishing classic probability results are discussed.

Front matter and Table of contents

Chapter 1: Introduction

Chapter 10: Conditional probability and expectation

  • — Christian Robert, Chance 2020
    "The book aims to cover the probability essentials for dealing with graduate-level statistics—in particular, convergence, conditioning, and paradoxes resulting from using non-rigorous approaches to probability. A range that completely fits my own prerequisite for statistics students in my classes and that, of course, involves recourse to (Lebesgue) measure theory, and a goal that I find both commendable and comforting,...." “If I had to teach this material to students, however, I would certainly rely on this book”

  • — Lumley, SIM 2017
    "Each chapter has a good set of exercises, and a summary of important points. Proschan and Shaw have written a useful textbook for introductory graduate or advanced undergraduate use, and one that should help statisticians see why probability is useful."

  • — Jordan M. Stoyanov, Zen tralblatt MATH 1353 2016
    "The material is well-chosen and structured. All notions and concepts of modern probability are discussed in the manner chosen by the authors. There is a substantial and rigorous mathematics used. The presentation is smooth.....students, teachers, and applied scientists will benefit a lot from this excellent book."