The Generalized Multiset Sampler: Theory and Its Application

• Activity Number: 289
• Type: Topic Contributed
• Date/Time: Tuesday, July 31, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Hang J Kim*+ and Steven MacEachern
• Companies: The Ohio State University and The Ohio State University
• Keywords: Advanced MCMC ; Metropolis ; Importance sampling ; Mixture model ; Multimodal distribution ; Mixing of chain

Abstract

It is well known that an ordinary MCMC sampler run on a multimodal limiting distribution can suffer from the local-trap problem -- that is, the chain is easily trapped in a local mode, essentially rarely or never escaping to visit other modes of the distribution. The multiset sampler (MSS) proposed by Leman et al. (2009) is a new MCMC algorithm to alleviate the local-trap problem by introducing a notion of multiset sampling distribution. We generalize the algorithm by re-defining the MSS with an explicit description of the link between target distribution and sampling distribution. Attention of our work is given to construction of Markov chain, the impact of tuning parameters on mixing of the chain, inference arising from the chain, theoretical properties of the chain, and general implementation issues. The performance is illustrated on a number of examples including a variance component model, Bayesian outlier detection and a gene expression study.