A Review of Multiple Try MCMC algorithms for Signal Processing

TL;DR

This paper reviews advanced multiple try MCMC algorithms used in signal processing, highlighting their benefits, limitations, and differences through numerical comparisons, to improve Bayesian inference in complex applications.

Contribution

It provides a comprehensive review and comparison of various multiple try MCMC methods, including their connections and unique features, for signal processing applications.

Findings

Multiple try techniques enhance exploration of the sample space.

Different MCMC methods show varied performance in numerical simulations.

The review clarifies the benefits and limitations of each method.

Abstract

Many applications in signal processing require the estimation of some parameters of interest given a set of observed data. More specifically, Bayesian inference needs the computation of {\it a-posteriori} estimators which are often expressed as complicated multi-dimensional integrals. Unfortunately, analytical expressions for these estimators cannot be found in most real-world applications, and Monte Carlo methods are the only feasible approach. A very powerful class of Monte Carlo techniques is formed by the Markov Chain Monte Carlo (MCMC) algorithms. They generate a Markov chain such that its stationary distribution coincides with the target posterior density. In this work, we perform a thorough review of MCMC methods using multiple candidates in order to select the next state of the chain, at each iteration. With respect to the classical Metropolis-Hastings method, the use of multiple try techniques foster the exploration of the sample space. We present different Multiple Try Metropolis schemes, Ensemble MCMC methods, Particle Metropolis-Hastings algorithms and the Delayed Rejection Metropolis technique. We highlight limitations, benefits, connections and differences among the different methods, and compare them by numerical simulations.