The Generalized Multiset Sampler

Abstract

The multiset sampler, an MCMC algorithm recently proposed by Leman and coauthors, is an easy-to-implement algorithm which is especially well-suited to drawing samples from a multimodal distribution. We generalize the algorithm by redefining the multiset sampler with an explicit link between target distribution and sampling distribution. The generalized formulation replaces the multiset with a K-tuple, which allows us to use the algorithm on unbounded parameter spaces, improves estimation, and sets up further extensions to adaptive MCMC techniques. Theoretical properties of the algorithm are provided and guidance is given on its implementation. Examples, both simulated and real, confirm that the generalized multiset sampler provides a simple, general and effective approach to sampling from multimodal distributions. Supplementary materials for this article are available online.

Key Words:

• Advanced MCMC
• Gene expression study
• Importance sampling
• Local trap
• Metropolis
• Mixture model

ACKNOWLEDGMENTS

The first author acknowledges support from National Science Foundation grant SES-11-31897. The second author acknowledges support from National Science Foundation grants DMS-1007682 and DMS-1209194. The authors thank the editors and referees for their constructive comments.