Optimal scaling of random walk Metropolis algorithms using Bayesian large-sample asymptotics

Sebastian M Schmon, Philippe Gagnon

Abstract:

High-dimensional asymptotics have been shown to be useful to derive tuning rules for finding the optimal
scaling in random walk Metropolis algorithms. The assumptions under which weak convergence results
are proved are however restrictive; the target density is typically assumed to be of a product form. Users
may thus doubt the validity of such tuning rules in practical applications. In this paper, we shed some
light on optimal scaling problems from a different perspective, namely a large-sample one. This allows to
prove weak convergence results under realistic assumptions and to propose novel parameter dimension
dependent tuning guidelines. The proposed guidelines are consistent with previous ones when the target
density is close to having a product form, but significantly different when this is not the case.