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Non-reversible guided Metropolis kernel

Part of: Markov processes Probabilistic methods, simulation and stochastic differential equations

Published online by Cambridge University Press:  12 April 2023

Kengo Kamatani Open the ORCID record for Kengo Kamatani [Opens in a new window]  and
Xiaolin Song
Kengo Kamatani*
Affiliation:
The Institute of Statistical Mathematics
Xiaolin Song*
Affiliation:
Osaka University
*
*Postal address: 10-3 Midori-cho, Tachikawa Tokyo 190-8562, Japan. Email address: kamatani@ism.ac.jp
**Postal address: Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama-cho, Toyonaka, Osaka, Japan. Email address: songxl@sigmath.es.osaka-u.ac.jp
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Abstract

We construct a class of non-reversible Metropolis kernels as a multivariate extension of the guided-walk kernel proposed by Gustafson (Statist. Comput. 8, 1998). The main idea of our method is to introduce a projection that maps a state space to a totally ordered group. By using Haar measure, we construct a novel Markov kernel termed the Haar mixture kernel, which is of interest in its own right. This is achieved by inducing a topological structure to the totally ordered group. Our proposed method, the $\Delta$-guided Metropolis–Haar kernel, is constructed by using the Haar mixture kernel as a proposal kernel. The proposed non-reversible kernel is at least 10 times better than the random-walk Metropolis kernel and Hamiltonian Monte Carlo kernel for the logistic regression and a discretely observed stochastic process in terms of effective sample size per second.

Keywords

Markov chain Monte CarloreversibilityHaar measureBayesian inference

MSC classification

Primary: 65C05: Monte Carlo methods 65C40: Computational Markov chains
Secondary: 60J05: Discrete-time Markov processes on general state spaces
Type
Original Article
Information
Journal of Applied Probability , Volume 60 , Issue 3 , September 2023 , pp. 955 - 981
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust

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