Bayesian inference for hidden Markov models under genuine multimodality with application to ecological time series

TL;DR

This paper addresses challenges in Bayesian inference for hidden Markov models with multimodal posteriors, proposing improved methods and priors, demonstrated on ecological time series data of blue whale dives.

Contribution

It identifies pitfalls in parallel tempering for HMMs, introduces new priors, and demonstrates their effectiveness on real ecological data.

Findings

Modified PT algorithm improves exploration of multimodal posteriors

New non-informative priors facilitate better Bayesian inference

Application to blue whale data reveals insights into movement patterns

Abstract

Bayesian inference in hidden Markov models (HMMs) can be challenging due to the presence of multimodality in the likelihood function, and consequently in the joint posterior distribution, even after correcting for label switching. The parallel tempering (PT) algorithm, a state-space augmentation method, is a widely used approach for dealing with multimodal distributions. Nevertheless, standard implementation of the PT algorithm may not always be sufficient to effectively explore the high-dimensional, complex multimodal posterior distributions that arise in HMMs. In this work, we demonstrate common pitfalls when implementing the PT algorithm for HMMs, approaches to remedy them, and introduce new non-informative prior distributions that facilitate effective posterior distribution exploration. We analyse time series of blue whale dive data with two 3-state HMMs in a Bayesian framework, one of which includes a categorical covariate in the transition probability matrix to account for the effect of sound stimuli on the whale's behavior. We demonstrate how effective implementation of the modified PT algorithm for Bayesian inference leads to effective exploration of the resultant multimodal posterior distribution and how that affects inference for the underlying movement patterns of the blue whales.