Adaptive Markov Chain Monte Carlo for Auxiliary Variable Method and Its Application to Parallel Tempering

TL;DR

This paper introduces an adaptive algorithm for auxiliary variable Markov Chain Monte Carlo methods, specifically applied to Parallel Tempering, which automatically tunes parameters to improve sampling efficiency from complex distributions.

Contribution

It proposes a novel adaptive parameter tuning algorithm for auxiliary variable MCMC methods and proves its convergence, enhancing the efficiency of Parallel Tempering.

Findings

Adaptive Parallel Tempering outperforms conventional algorithms.

The proposed method effectively tunes parameters during sampling.

Validation shows improved sampling from complex distributions.

Abstract

Auxiliary variable methods such as the Parallel Tempering and the cluster Monte Carlo methods generate samples that follow a target distribution by using proposal and auxiliary distributions. In sampling from complex distributions, these algorithms are highly more efficient than the standard Markov chain Monte Carlo methods. However, their performance strongly depends on their parameters and determining the parameters is critical. In this paper, we proposed an algorithm for adapting the parameters during drawing samples and proved the convergence theorem of the adaptive algorithm. We applied our algorithm to the Parallel Tempering. That is, we developed adaptive Parallel Tempering that tunes the parameters on the fly. We confirmed the effectiveness of our algorithm through the validation of the adaptive Parallel Tempering, comparing samples from the target distribution by the adaptive Parallel Tempering and samples by conventional algorithms.