An improved sampler for recursive Bayesian inference

Music City Center 

Recursive Bayesian inference is an important tool for applications in which data arrives sequentially and updated parameter estimates are desired each time data arrives. Models for which the posterior distribution is estimated via Markov chain Monte Carlo (MCMC) can use Prior-Proposal-Recursive Bayes (PPRB) to resample existing posterior samples using the likelihood of the new data. Like all filtering methods, if applied many times PPRB will eventually converge to sampling from a degenerate distribution, limiting its usefulness for repeated application in longitudinal data settings. We present a sampling strategy for recursive Bayesian inference that extends PPRB to avoid the eventual tendency towards degeneracy by the addition of a transition kernel step run in parallel on each filtered sample. We show that this sampler improves upon PPRB by producing samples from the target posterior distribution that will not tend towards degeneracy. Additionally, we compare the performance of the proposed sampler to other streaming samplers for recursive inference and present an application to Ecological species count data.

Recursive Bayes

Distributed MCMC

Streaming Data