Issues in the Multiple Try Metropolis mixing

TL;DR

This paper examines the limitations of the Multiple Try Metropolis algorithm's mixing efficiency, identifies scenarios where increasing tries does not improve performance, and proposes solutions to address these issues.

Contribution

It analyzes scenarios where increasing tries in MTM does not enhance performance and introduces solutions to improve mixing efficiency.

Findings

Increasing tries does not always improve MTM performance.

Certain scenarios hinder the benefits of more tries.

Proposed solutions can mitigate mixing issues.

Abstract

The multiple Try Metropolis (MTM) algorithm is an advanced MCMC technique based on drawing and testing several candidates at each iteration of the algorithm. One of them is selected according to certain weights and then it is tested according to a suitable acceptance probability. Clearly, since the computational cost increases as the employed number of tries grows, one expects that the performance of an MTM scheme improves as the number of tries increases, as well. However, there are scenarios where the increase of number of tries does not produce a corresponding enhancement of the performance. In this work, we describe these scenarios and then we introduce possible solutions for solving these issues.