Efficient Metropolis Jumping Rules

Abstract The algorithm of Metropolis et al. (1953) and its generalizations have been increasingly popular in computational physics and, more recently, statistics, for sampling from intractable multivariate distributions. Much recent research has been devoted to increasing the efficiency of simulation algorithms by altering the jumping rules for Metropolis-like algorithms. We study a very specific question: What are the most efficient symmetric jumping kernels for simulating a normal target distribution using the Metropolis algorithmã We provide a general theoretical result as the dimension of a class of canonical problems goes to ∞ and numerical approximations and simulations for low-dimensional Gaussian target distributions that show that the limiting results provide extremely accurate approximations in six and higher dimensions.