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2018 Hitting time and mixing time bounds of Stein’s factors
Michael C.H. Choi
Electron. Commun. Probab. 23: 1-10 (2018). DOI: 10.1214/18-ECP110

Abstract

For any discrete target distribution, we exploit the connection between Markov chains and Stein’s method via the generator approach and express the solution of Stein’s equation in terms of expected hitting time. This yields new upper bounds of Stein’s factors in terms of the parameters of the Markov chain, such as mixing time and the gradient of expected hitting time. We compare the performance of these bounds with those in the literature, and in particular we consider Stein’s method for discrete uniform, binomial, geometric and hypergeometric distribution. As another application, the same methodology applies to bound expected hitting time via Stein’s factors. This article highlights the interplay between Stein’s method, modern Markov chain theory and classical fluctuation theory.

Citation

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Michael C.H. Choi. "Hitting time and mixing time bounds of Stein’s factors." Electron. Commun. Probab. 23 1 - 10, 2018. https://doi.org/10.1214/18-ECP110

Information

Received: 15 August 2017; Accepted: 16 January 2018; Published: 2018
First available in Project Euclid: 15 February 2018

zbMATH: 1390.60281
MathSciNet: MR3771764
Digital Object Identifier: 10.1214/18-ECP110

Subjects:
Primary: 60J27 , 60J45 , 60J75

Keywords: eigentime , hitting time , mixing time , stationary time , Stein’s factor , Stein’s method

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