Rate optimality of Random walk Metropolis algorithm in high-dimension with heavy-tailed target distribution

摘要

The choice of the increment distribution is crucial for the random-walkMetropolis-Hastings (RWM) algorithm. In this paper we study the optimal choicein high-dimension setting among all possible increment distributions. Theconclusion is rather counter intuitive, but the optimal rate of convergence isattained by the usual choice, the normal distribution as the incrementdistribution. In particular, no heavy-tailed increment distribution can improvethe rate.