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 that 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 detail 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.
|Title of host publication||Wiley StatsRef: Statistics Reference Online|
|Editors||N. Balakrishnan, Theodore Colton, Brian Everitt, Walter Piegorsch, Fabrizio Ruggeri, Jozef L. Teugels|
|Publisher||John Wiley & Sons Inc.|
|Publication status||Published - 15 May 2017|