Plateau Proposal Distributions for Adaptive Component-wise Multiple-Try Metropolis

TL;DR

This paper introduces Plateau proposal distributions for component-wise multiple-try Metropolis MCMC, enhancing sampling efficiency from complex, multi-modal, and correlated distributions through adaptive, non-overlapping proposals.

Contribution

The paper proposes a new class of non-overlapping Plateau proposal distributions for MCMC, enabling more efficient exploration of complex target distributions.

Findings

Outperforms existing methods on complex, multi-modal distributions

Improves burn-in and convergence properties

Enhances exploration of correlated components

Abstract

Markov chain Monte Carlo (MCMC) methods are sampling methods that have become a commonly used tool in statistics, for example to perform Monte Carlo integration. As a consequence of the increase in computational power, many variations of MCMC methods exist for generating samples from arbitrary, possibly complex, target distributions. The performance of an MCMC method is predominately governed by the choice of the so-called proposal distribution used. In this paper, we introduce a new type of proposal distribution for the use in MCMC methods that operates component-wise and with multiple trials per iteration. Specifically, the novel class of proposal distributions, called Plateau distributions, do not overlap, thus ensuring that the multiple trials are drawn from different regions of the state space. Furthermore, the Plateau proposal distributions allow for a bespoke adaptation procedure that lends itself to a Markov chain with efficient problem dependent state space exploration and improved burn-in properties. Simulation studies show that our novel MCMC algorithm outperforms competitors when sampling from distributions with a complex shape, highly correlated components or multiple modes.