Weighted particle tempering

Abstract

The application of Bayesian methods often requires Metropolis–Hastings or related algorithms to sample from an intractable posterior distribution. In especially challenging cases, such as with strongly correlated parameters or multimodal posteriors, exotic forms of Metropolis–Hastings are preferred for generating samples within a reasonable time. These algorithms require nontrivial and often prohibitive tuning, with little or no performance guarantees. In light of this difficulty, a new, parallelizable algorithm called weighted particle tempering is introduced. Weighted particle tempering is easily tuned and suitable for a broad range of applications. The algorithm works by running multiple random walk Metropolis chains directed at a tempered version of the target distribution, weighting the iterates and resampling. The algorithm’s performance monotonically improves with more of these underlying chains, a feature that simplifies tuning. Through the use of simulation studies, weighted particle tempering is shown to outperform two similar methods: parallel tempering and parallel hierarchical sampling. In addition, two case studies are explored: breast cancer classification and graphical models for financial data.