The Self-Multiset Sampler

ABSTRACT

The multiset sampler has been shown to be an effective algorithm to sample from complex multimodal distributions, but the multiset sampler requires that the parameters in the target distribution can be divided into two parts: the parameters of interest and the nuisance parameters. We propose a new self-multiset sampler (SMSS), which extends the multiset sampler to distributions without nuisance parameters. We also generalize our method to distributions with unbounded or infinite support. Numerical results show that the SMSS and its generalization have a substantial advantage in sampling multimodal distributions compared to the ordinary Markov chain Monte Carlo algorithm and some popular variants. Supplemental materials for the article are available online.

Keywords:

• Data augmentation
• Metropolis–Hastings algorithm
• Multimodal
• Multiset

Acknowledgments

The authors thank the editor, the associate editor, and two referees for helpful suggestions. This work was supported in part by National Science Foundation grant DMS-1406455 and National Natural Science Foundation of China Grant 11501123.