Sequential Monte Carlo with transformations

Richard G Everitt,Daniel J Wilson,Felipe Medina-Aguayo,Richard Culliford

doi:10.1007/s11222-019-09903-y

Abstract

This paper examines methodology for performing Bayesian inference sequentially on a sequence of posteriors on spaces of different dimensions. For this, we use sequential Monte Carlo samplers, introducing 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 is low. We use this approach on model comparison for mixture models, and for inferring coalescent trees sequentially, as data arrives.

Highlights

1.1 Sequential inferenceMuch of the methodology for Bayesian computation is designed with the aim of approximating a posterior π
This paper introduces a sequential technique for Bayesian model comparison and parameter estimation, and an approach to online parameter and marginal likelihood estimation for the coalescent, underpinned by the same methodological development: transformation SMC (TSMC)
One innovation introduced in the paper is the use of transformations within SMC for creating proposal distributions when moving between dimensions

Summary

Introduction

1.1 Sequential inferenceMuch of the methodology for Bayesian computation is designed with the aim of approximating a posterior π. We describe the use of TSMC for online inference under the coalescent model in population genetics (Kingman 1982); we consider the case in which we wish to infer the clonal ancestry (or ancestral tree) of a bacterial population from DNA sequence data. Current approaches in this area use MCMC (Drummond and Rambaut 2007), which is a limitation in situations where DNA sequence data does not arrive as a batch, such as may happen when studying the spread of an infectious disease as the outbreak is progressing (Didelot et al 2014). Our approach yields more stable estimates of the marginal likelihood of models than current approaches used (a) μ1 (birth). (c) μ2 (birth)

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Conclusion