ABSTRACT
TheMetropolis-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 hocmanner involving much trial and error. However, it is also possible to use theory to estimate optimal proposal scalings and/or adaptive algorithms to attempt to find good proposals automatically. This chapter reviews both of these possibilities.
