Using Markov transition matrices to generate trial configurations in Markov chain Monte Carlo simulations

TL;DR

This paper introduces a novel Markov chain Monte Carlo method that uses transition matrices to generate trial configurations, enhancing sampling quality and applicability to polymer configuration sampling.

Contribution

The paper presents two new algorithms utilizing Markov transition matrices for MCMC, with derived acceptance rules and analysis of sampling quality factors.

Findings

Effective sampling of polymer configurations demonstrated

Improved Monte Carlo algorithm portability shown

New generative model design potential identified

Abstract

We propose a new Markov chain Monte Carlo method in which trial configurations are generated by evolving a state, sampled from a prior distribution, using a Markov transition matrix. We present two prototypical algorithms and derive their corresponding acceptance rules. We first identify the important factors controlling the quality of the sampling. We then apply the method to the problem of sampling polymer configurations with fixed endpoints. Applications of the proposed method range from the design of new generative models to the improvement of the portability of specific Monte Carlo algorithms, like configurational-bias schemes.