Interacting Multiple Try Algorithms with Different Proposal Distributions

TL;DR

This paper introduces an interacting multiple-try MCMC algorithm with different proposal distributions, enhancing sampling efficiency and exploration capabilities compared to traditional methods.

Contribution

It extends the multiple-try Metropolis algorithm by incorporating diverse proposal distributions and an interaction mechanism, broadening the scope of population Monte Carlo methods.

Findings

The new algorithm performs better than basic MTM in numerical tests.

Interaction mechanism improves state space exploration.

Algorithm validity and proposal choices are discussed.

Abstract

We propose a new class of interacting Markov chain Monte Carlo (MCMC) algorithms designed for increasing the efficiency of a modified multiple-try Metropolis (MTM) algorithm. The extension with respect to the existing MCMC literature is twofold. The sampler proposed extends the basic MTM algorithm by allowing different proposal distributions in the multiple-try generation step. We exploit the structure of the MTM algorithm with different proposal distributions to naturally introduce an interacting MTM mechanism (IMTM) that expands the class of population Monte Carlo methods. We show the validity of the algorithm and discuss the choice of the selection weights and of the different proposals. We provide numerical studies which show that the new algorithm can perform better than the basic MTM algorithm and that the interaction mechanism allows the IMTM to efficiently explore the state space.