Metropolis Sampling
This is an incremental review paper for researchers and practitioners in fields like Bayesian inference and optimization.
The paper provides a detailed overview of the Metropolis-Hastings sampler, describing its elements, variants, and recent extensions to offer an exhaustive overview of current Metropolis-based sampling techniques.
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.