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Ergodicity of Markov chain Monte Carlo with reversible proposal (1602.02889v1)
Published 9 Feb 2016 in stat.ME, math.ST, and stat.TH
Abstract: We describe ergodic properties of some Metropolis-Hastings (MH) algorithms for heavy-tailed target distributions. The analysis usually falls into sub-geometric ergodicity 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 the MpCN algorithm becomes a random-walk Metropolis algorithm under suitable transformation.