Sequential Monte Carlo with transformations

TL;DR

This paper presents a flexible sequential Monte Carlo method using deterministic transformations for Bayesian inference across models of varying dimensions, improving efficiency and applicability in model comparison and coalescent tree inference.

Contribution

It introduces a novel SMC approach with deterministic transformations to handle different-dimensional posteriors, enhancing Bayesian model comparison methods.

Findings

Effective in mixture model comparison

Applicable to sequential coalescent tree inference

Outperforms traditional RJMCMC in low acceptance scenarios

Abstract

This paper introduces methodology for performing Bayesian inference sequentially on a sequence of posteriors on spaces of different dimensions. We show how this may be achieved through the use of sequential Monte Carlo (SMC) samplers (Del Moral et al., 2006, 2007), making use of the full flexibility of this framework in order that the method is computationally efficient. In particular, we introduce the innovation of using deterministic transformations to move particles effectively between target distributions with different dimensions. This approach, combined with adaptive methods, yields an extremely flexible and general algorithm for Bayesian model comparison that is suitable for use in applications where the acceptance rate in reversible jump Markov chain Monte Carlo (RJMCMC) is low. We demonstrate this approach on the well-studied problem of model comparison for mixture models, and for the novel application of inferring coalescent trees sequentially, as data arrives.