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2022 Stein’s Method Meets Computational Statistics: A Review of Some Recent Developments
Andreas Anastasiou, Alessandro Barp, François-Xavier Briol, Bruno Ebner, Robert E. Gaunt, Fatemeh Ghaderinezhad, Jackson Gorham, Arthur Gretton, Christophe Ley, Qiang Liu, Lester Mackey, Chris J. Oates, Gesine Reinert, Yvik Swan
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Statist. Sci. Advance Publication 1-20 (2022). DOI: 10.1214/22-STS863


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.

Funding Statement

AA was supported by a start-up grant from the University of Cyprus. AB was supported by the UK Defence Science and Technology Laboratory (Dstl) and Engineering and Physical Research Council (EPSRC) under the grant EP/R018413/2. FXB and CJO were supported by the Lloyds Register Foundation Programme on Data-Centric Engineering and The Alan Turing Institute under the EPSRC grant EP/N510129/1. AG was supported by the Gatsby Charitable Foundation. RG was supported by a Dame Kathleen Ollerenshaw Research Fellowship. FG and CL were supported by a BOF Starting Grant of Ghent University. QL was supported in part by NSF CAREER No. 1846421. GR was supported in part by EP/T018445/1 and EP/R018472/1. YS was supported in part by CDR/OL J.0197.20 from FRS-FNRS.


The authors thank the Editor, Associate Editor and two anonymous reviewers for helpful comments that led to a clear improvement of the presentation of this paper.

Christophe Ley is the corresponding author.


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Andreas Anastasiou. Alessandro Barp. François-Xavier Briol. Bruno Ebner. Robert E. Gaunt. Fatemeh Ghaderinezhad. Jackson Gorham. Arthur Gretton. Christophe Ley. Qiang Liu. Lester Mackey. Chris J. Oates. Gesine Reinert. Yvik Swan. "Stein’s Method Meets Computational Statistics: A Review of Some Recent Developments." Statist. Sci. Advance Publication 1 - 20, 2022.


Published: 2022
First available in Project Euclid: 28 October 2022

Digital Object Identifier: 10.1214/22-STS863

Keywords: approximate Markov chain Monte Carlo , control variates , goodness-of-fit testing , likelihood ratio , maximum likelihood estimator , prior sensitivity , sample quality , Stein’s method , variational inference

Rights: Copyright © 2022 Institute of Mathematical Statistics


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