UNDERSTANDING THE METROPOLIS-HASTINGS ALGORITHM

We provide a detailed, introductory exposition of the Metropolis-Hasti ngs algorithm, a powerful Markov chain method to simulate multivariate distributions. A simple, intuitive derivation of this method is given along with guidance on implementation. Also discussed are two applica tions of the algorithm, one for implementing acceptance-rejection samp ling when a blanketing function is not available and the other for imp lementing the algorithm with block-at-a-time scans. In the latter situ ation, many different algorithms, including the Gibbs sampler, are sho wn to be special cases of the Metropolis-Hastings algorithm. The metho ds are illustrated with examples.