Efficient Markov Chain Monte Carlo Sampling for Hierarchical Hidden Markov Models

TL;DR

This paper introduces combined computational methods that significantly enhance MCMC sampling efficiency for hierarchical hidden Markov models, enabling faster and more scalable Bayesian inference in complex ecological and other embedded HMM applications.

Contribution

The paper develops and tests a novel combination of existing and new algorithms for efficient MCMC sampling in hierarchical HMMs, applicable across various fields.

Findings

Several orders of magnitude improvement in sampling efficiency

Effective for ecological capture-recapture models

Applicable to any embedded discrete HMMs

Abstract

Traditional Markov chain Monte Carlo (MCMC) sampling of hidden Markov models (HMMs) involves latent states underlying an imperfect observation process, and generates posterior samples for top-level parameters concurrently with nuisance latent variables. When potentially many HMMs are embedded within a hierarchical model, this can result in prohibitively long MCMC runtimes. We study combinations of existing methods, which are shown to vastly improve computational efficiency for these hierarchical models while maintaining the modeling flexibility provided by embedded HMMs. The methods include discrete filtering of the HMM likelihood to remove latent states, reduced data representations, and a novel procedure for dynamic block sampling of posterior dimensions. The first two methods have been used in isolation in existing application-specific software, but are not generally available for incorporation in arbitrary model structures. Using the NIMBLE package for R, we develop and test combined computational approaches using three examples from ecological capture-recapture, although our methods are generally applicable to any embedded discrete HMMs. These combinations provide several orders of magnitude improvement in MCMC sampling efficiency, defined as the rate of generating effectively independent posterior samples. In addition to being computationally significant for this class of hierarchical models, this result underscores the potential for vast improvements to MCMC sampling efficiency which can result from combinations of known algorithms.