An adaptive multiple-try Metropolis algorithm

Abstract

Markov chain Monte Carlo (MCMC) methods, specifically samplers based on random walks, often have difficulty handling target distributions with complex geometry such as multi-modality. We propose an adaptive multiple-try Metropolis algorithm designed to tackle such problems by combining the flexibility of multiple-proposal samplers with the user-friendliness and optimality of adaptive algorithms. We prove the ergodicity of the resulting Markov chain with respect to the target distribution using common techniques in the adaptive MCMC literature. In a Bayesian model for loss of heterozygosity in cancer cells, we find that our method outperforms traditional adaptive samplers, non-adaptive multiple-try Metropolis samplers, and various more sophisticated competing methods.