A multi-point Metropolis scheme with generic weight functions

TL;DR

This paper introduces a flexible multi-point Metropolis algorithm allowing arbitrary weight functions, enhancing the design of efficient MCMC samplers with proven balance and practical validation.

Contribution

It proposes a generalized multi-point Metropolis scheme with arbitrary weight functions, expanding the flexibility and understanding of MCMC algorithms.

Findings

The method satisfies the detailed balance condition.

Numerical simulations demonstrate the effectiveness of the approach.

Provides new insights into MCMC algorithm relationships.

Abstract

The multi-point Metropolis algorithm is an advanced MCMC technique based on drawing several correlated samples at each step and choosing one of them according to some normalized weights. We propose a variation of this technique where the weight functions are not specified, i.e., the analytic form can be chosen arbitrarily. This has the advantage of greater flexibility in the design of high-performance MCMC samplers. We prove that our method fulfills the balance condition, and provide a numerical simulation. We also give new insight into the functionality of different MCMC algorithms, and the connections between them.