The Metropolis‐Hastings Algorithm

This chapter presents a description of the basic Metropolis-Hastings (MH) algorithm, and then considers its variants, such as the Hit-and-Run algorithm, the Langevin algorithm, the multiple-try MH algorithm, the reversible jump MH algorithm, and the Metropolis-within-Gibbs sampler. It also considers two applications, the change-point identification and ChIP-chip data analysis. The chapter then describes several MH schemes that improve the mixing of the MH chain in certain scenarios. When some components cannot be easily simulated, rather than resorting to a customized algorithm such as the acceptance-rejection algorithm, Muller suggests a compromised Gibbs algorithm – the Metropolis-within-Gibbs sampler. Controlled Vocabulary Terms Gibbs sampling; Markov chain; Metropolis-Hastings algorithm