Weighted particle tempering

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.