Stein's Method Meets Computational Statistics: A Review of Some Recent Developments

Stein's method compares probability distributions through the study of a class of linear operators called Stein operators. While mainly stud-ied in probability and used to underpin theoretical statistics, Stein's method has led to significant advances in computational statistics in recent years. The goal of this survey is to bring together some of these recent develop-ments, and in doing so, to stimulate further research into the successful field of Stein's method and statistics. The topics we discuss include tools to bench-mark and compare sampling methods such as approximate Markov chain Monte Carlo, deterministic alternatives to sampling methods, control variate techniques, parameter estimation and goodness-of-fit testing.