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

by   Andreas Anastasiou, et al.

Stein's method is a collection of tools for analysing distributional comparisons through the study of a class of linear operators called Stein operators. Originally studied in probability, Stein's method has also enabled some important developments in statistics. This early success has led to a high research activity in this area in recent years. The goal of this survey is to bring together some of these developments in theoretical statistics as well as in computational statistics and, in doing so, to stimulate further research into the successful field of Stein's method and statistics. The topics we discuss include: explicit error bounds for asymptotic approximations of estimators and test statistics, a measure of prior sensitivity in Bayesian statistics, tools to benchmark and compare sampling methods such as approximate Markov chain Monte Carlo, deterministic alternatives to sampling methods, control variate techniques, and goodness-of-fit testing.



There are no comments yet.


page 1

page 2

page 3

page 4


Bayesian Computing in the Statistics and Data Science Curriculum

Bayesian statistics has gained great momentum since the computational de...

Subsampling MCMC - A review for the survey statistician

The rapid development of computing power and efficient Markov Chain Mont...

Bayesian Restricted Likelihood Methods: Conditioning on Insufficient Statistics in Bayesian Regression

Bayesian methods have proven themselves to be successful across a wide r...

Regularization and Bayesian Learning in Dynamical Systems: Past, Present and Future

Regularization and Bayesian methods for system identification have been ...

Three rates of convergence or separation via U-statistics in a dependent framework

Despite the ubiquity of U-statistics in modern Probability and Statistic...

Recent advances in directional statistics

Mainstream statistical methodology is generally applicable to data obser...

Julian Ernst Besag, 26 March 1945 -- 6 August 2010, a biographical memoir

Julian Besag's contributions to the discipline of statistics are profoun...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.