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2018 Fast mixing of metropolis-hastings with unimodal targets
James Johndrow, Aaron Smith
Electron. Commun. Probab. 23: 1-9 (2018). DOI: 10.1214/18-ECP170

Abstract

A well-known folklore result in the MCMC community is that the Metropolis-Hastings algorithm mixes quickly for any unimodal target, as long as the tails are not too heavy. Although we’ve heard this fact stated many times in conversation, we are not aware of any quantitative statement of this result in the literature, and we are not aware of any quick derivation from well-known results. The present paper patches this small gap in the literature, providing a generic bound based on the popular “drift-and-minorization” framework of [19]. Our main contribution is to study two sublevel sets of the Lyapunov function and use path arguments in order to obtain a sharper bound than what can typically be obtained from multistep minorization arguments.

Citation

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James Johndrow. Aaron Smith. "Fast mixing of metropolis-hastings with unimodal targets." Electron. Commun. Probab. 23 1 - 9, 2018. https://doi.org/10.1214/18-ECP170

Information

Received: 28 July 2018; Accepted: 23 September 2018; Published: 2018
First available in Project Euclid: 16 October 2018

zbMATH: 06964414
MathSciNet: MR3866044
Digital Object Identifier: 10.1214/18-ECP170

Subjects:
Primary: 60J05

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