Non-reversible Metropolis-Hastings
type: Item
instance of: scholarly article
title: Non-reversible Metropolis-Hastings
zbMATH Open document ID: 1360.65040
author: Joris Bierkens
published in: Statistics and Computing
publication date: 2016-11-16T00:00:00Z
full work available at URL: https://arxiv.org/abs/1401.8087
review text: The Metropolis-Hastings (MH) algorithm is a Markov chain Monte Carlo (MCMC) method of profound importance to many fields of mathematics such as Bayesian inference and statistical mechanics. In the present paper, an application of the non-reversible Metropolis-Hastings (NRMH) method in continuous setting by developing the necessary theory and applying, as first examples, the theory of Gaussian distribution in three and nine dimensions is provided. The empirical autocorrelation and estimated asymptotic variance for NRMH applied to these examples show significant improvement compared to MH with identical step-size. There exist two basic approaches to the construction of non-reversible chains from reversible chains. In the present paper, the approach of the non-reversibility without altering the state space is constructed. The MH is extended to NRMH which allows non-reversible transition. In Section 2, the notion of vorticity matrix is recalled. The non-reversible Markov chains are given in the terms of the vorticity. In Subsection 2.3, the concept of the non-reversible Hastings algorithm to construct Markov chains is discussed. In Section 3, the advantages of non-reversible Markov chains in finite state are briefly discussed. It is shown how to transform a discrete time Markov chain into a continuous time chain. In Section 4, it is explained how to extend the idea of non-reversible MH algorithm to an Euclidean state space. In Subsection 4.2, the use of the Langevin diffusions for simulating from a target density and the potential role of NRMH in within are discussed. The concept of the Euler-Maruyama discretization of the Langevin diffusion is developed. In Subsection 4.3, the NRMH method is applied to sampling multivariate Gaussian distributions. In Subsection 4.4, the concept of the empirical autocorrelation function (EACF) is given. The EACF for 3-dimensional and 9-dimensional examples are considered. The performance of NRMH is compared to MH with identical step-siz…
Mathematics Subject Classification ID: 65C40
Mathematics Subject Classification ID: 60J20
Mathematics Subject Classification ID: 60J22
Mathematics Subject Classification ID: 65C50
Mathematics Subject Classification ID: 65C60
Mathematics Subject Classification ID: 65C05
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 62F15
Mathematics Subject Classification ID: 82C80
zbMATH DE Number: 6653297
zbMATH Keywords: Markov Chain Monte Carlo
zbMATH Keywords: Metropolis-Hastings
zbMATH Keywords: non-reversible Markov processes
zbMATH Keywords: asymptotic variance
zbMATH Keywords: large deviation
zbMATH Keywords: Langevin sampling
zbMATH Keywords: Bayesian inference
zbMATH Keywords: empirical autocorrelation function
zbMATH Keywords: algorithm
reviewed by: Vassil Grozdanov
MaRDI profile type: Publication
OpenAlex ID: W3103728018
Wikidata QID: Q59474056
arXiv ID: 1401.8087
cites work: Accelerating reversible Markov chains
cites work: Lifting Markov chains to speed up mixing
cites work: Large deviations
cites work: Analysis of a nonreversible Markov chain sampler.
cites work: The Markov chain Monte Carlo revolution
cites work: What do we know about the Metropolis algorithm?
cites work: Q4527097
cites work: Monte Carlo sampling methods using Markov chains and their applications
cites work: Accelerating Gaussian diffusions
cites work: Q3998992
cites work: Optimal non-reversible linear drift for the convergence to equilibrium of a diffusion
cites work: Q3549475
cites work: Q3222981
cites work: Equation of State Calculations by Fast Computing Machines
cites work: Q3172405
cites work: Irreversible Langevin samplers and variance reduction: a large deviations approach
cites work: Optimal Scaling of Discrete Approximations to Langevin Diffusions
cites work: General state space Markov chains and MCMC algorithms
cites work: Exponential convergence of Langevin distributions and their discrete approximations
cites work: Q4340161
cites work: Irreversible Monte Carlo algorithms for efficient sampling
cites work: Q3874718
DBLP publication ID: journals/sac/Bierkens16
DOI: 10.1007/S11222-015-9598-X
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description: scientific article; zbMATH DE number 6653297