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

TL;DR

This survey reviews recent advances in Stein's method and its applications in computational statistics, highlighting tools for benchmarking sampling methods, parameter estimation, and goodness-of-fit testing.

Contribution

It consolidates recent developments in applying Stein's method to computational statistics, encouraging further research in this interdisciplinary area.

Findings

Enhanced benchmarking tools for sampling methods

Development of deterministic alternatives to sampling

Improved techniques for parameter estimation and testing

Abstract

Stein's method compares probability distributions through the study of a class of linear operators called Stein operators. While mainly studied 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 developments 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 benchmark 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.