Metropolis Sampling

TL;DR

This paper provides a comprehensive overview of the Metropolis-Hastings algorithm, a fundamental Markov Chain Monte Carlo method, including its basic principles, variants, and recent advancements in the field.

Contribution

It offers an exhaustive summary of the Metropolis-Hastings sampler, detailing its components, variants, and recent improvements, serving as a valuable reference for researchers and practitioners.

Findings

Detailed description of the MH algorithm and variants

Discussion of recent extensions and improvements

Overview of the algorithm's applications in Bayesian inference

Abstract

Monte Carlo (MC) sampling methods are widely applied in Bayesian inference, system simulation and optimization problems. The Markov Chain Monte Carlo (MCMC) algorithms are a well-known class of MC methods which generate a Markov chain with the desired invariant distribution. In this document, we focus on the Metropolis-Hastings (MH) sampler, which can be considered as the atom of the MCMC techniques, introducing the basic notions and different properties. We describe in details all the elements involved in the MH algorithm and the most relevant variants. Several improvements and recent extensions proposed in the literature are also briefly discussed, providing a quick but exhaustive overview of the current Metropolis-based sampling's world.