Optimal proposal distributions and adaptive MCMC

Abstract

Abstract. We review recent work concerning optimal proposal scalings for Metropolis-Hastings MCMC algorithms, and adaptive MCMC algorithms for trying to improve the algorithm on the fly. 1. Introduction. The Metropolis-Hastings algorithm (Metropolis et al., 1953; Hastings, 1970) requires choice of proposal distributions, and it is well-known that some proposals work much better than others. Determining which proposal is best for a particular target distribution is both very important and very difficult. Often this problem is attacked in an ad hoc manne