Adaptive Component-wise Multiple-Try Metropolis Sampling

TL;DR

This paper introduces an adaptive component-wise multiple-try Metropolis algorithm that dynamically selects and improves proposal distributions during sampling, enhancing efficiency for irregular target distributions.

Contribution

It proposes a novel adaptive CMTM algorithm that automatically chooses from multiple proposals and adapts over time, with proven ergodicity and demonstrated performance improvements.

Findings

Enhanced sampling efficiency for irregular distributions

Theoretical proof of ergodicity of the adaptive method

Improved results in simulations and real data applications

Abstract

One of the most widely used samplers in practice is the component-wise Metropolis-Hastings (CMH) sampler that updates in turn the components of a vector valued Markov chain using accept-reject moves generated from a proposal distribution. When the target distribution of a Markov chain is irregularly shaped, a `good' proposal distribution for one part of the state space might be a `poor' one for another part of the state space. We consider a component-wise multiple-try Metropolis (CMTM) algorithm that can automatically choose from a set of candidate moves sampled from different distributions. The computational efficiency is increased using an adaptation rule for the CMTM algorithm that dynamically builds a better set of proposal distributions as the Markov chain runs. The ergodicity of the adaptive chain is demonstrated theoretically. The performance is studied via simulations and real data examples.