On the flexibility of the design of Multiple Try Metropolis schemes

TL;DR

This paper explores the flexible design options of Multiple Try Metropolis (MTM) algorithms, demonstrating their adaptability while maintaining detailed balance through various extensions and numerical experiments.

Contribution

It highlights the versatility of MTM schemes and discusses multiple design possibilities that preserve detailed balance, supported by numerical results.

Findings

MTM schemes can be designed with various configurations.

Different extensions of MTM maintain detailed balance.

Numerical experiments illustrate the effectiveness of flexible MTM designs.

Abstract

The Multiple Try Metropolis (MTM) method is a generalization of the classical Metropolis-Hastings algorithm in which the next state of the chain is chosen among a set of samples, according to normalized weights. In the literature, several extensions have been proposed. In this work, we show and remark upon the flexibility of the design of MTM-type methods, fulfilling the detailed balance condition. We discuss several possibilities and show different numerical results.