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

2026-04-27

AI Summary

This study addresses the challenges posed by the intrinsically multimodal likelihood function in Bayesian inference for hidden Markov models (HMMs), which often leads to complex posterior distributions that are difficult to explore efficiently. To overcome this issue, the authors enhance parallel tempering to avoid common pitfalls in HMM settings and introduce a novel non-informative prior formulation, substantially improving sampling efficiency in high-dimensional, multimodal posterior spaces. The proposed framework further incorporates categorical covariates into the modeling of transition probabilities, enabling a detailed analysis of blue whale diving behavior time series. This approach accurately captures behavioral state transitions and quantifies the effects of acoustic stimuli, thereby achieving effective inference of the true multimodal posterior structure.

Technology Category

• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

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.

Problem

• Bayesian inference
• hidden Markov models
• multimodality
• parallel tempering
• ecological time series

Innovation

• Parallel Tempering
• Hidden Markov Models
• Multimodal Posterior
• Non-informative Priors
• Bayesian Inference