Eigenvalue analysis of an irreversible random walk with skew detailed balance conditions

TL;DR

This paper extends an irreversible MCMC algorithm with skew detailed balance to general discrete systems and analyzes its efficiency improvements through eigenvalue analysis of relaxation dynamics.

Contribution

It introduces a generalized irreversible MCMC method based on skew detailed balance and provides analytical evaluation of its efficiency in one-dimensional random walks.

Findings

Irreversible MCMC improves performance with proper parameter choices.

Eigenvalue analysis reveals faster relaxation modes.

Asymptotic variance is reduced by the proposed method.

Abstract

An irreversible Markov-chain Monte Carlo (MCMC) algorithm with skew detailed balance conditions originally proposed by Turitsyn et al. is extended to general discrete systems on the basis of the Metropolis-Hastings scheme. To evaluate the efficiency of our proposed method, the relaxation dynamics of the slowest mode and the asymptotic variance are studied analytically in a random walk on one dimension. It is found that the performance in irreversible MCMC methods violating the detailed balance condition is improved by appropriately choosing parameters in the algorithm.