ERGODICITY OF MARKOV CHAIN MONTE CARLO WITH REVERSIBLE PROPOSAL

摘要

We describe the ergodic properties of some Metropolis-Hastings algorithms for heavy-tailed target distributions. The results of these algorithms are usually analyzed under a subgeometric ergodic framework, but we prove that the mixed preconditioned Crank-Nicolson (MpCN) algorithm has geometric ergodicity even for heavy-tailed target distributions. This useful property comes from the fact that, under a suitable transformation, the MpCN algorithm becomes a random-walk Metropolis algorithm.