Efficient Bayesian model selection for coupled hidden Markov models with application to infectious diseases

TL;DR

This paper introduces a specialized Bayesian model selection method for coupled hidden Markov models with low inter-chain dependencies, enabling efficient analysis of infectious disease spread among individuals, demonstrated on avian influenza data.

Contribution

The authors develop a novel proposal distribution approach for CHMMs that is computationally feasible for high-dimensional problems with weak inter-chain dependencies.

Findings

Effective proposal distributions for CHMMs with many chains

Application to infectious disease modeling in chickens

Demonstrated efficiency on avian influenza data

Abstract

Performing model selection for coupled hidden Markov models (CHMMs) is highly challenging, owing to the large dimension of the hidden state process. Whilst in principle the hidden state process can be marginalized out via forward filtering, in practice the computational cost of doing so increases exponentially with the number of coupled Markov chains, making this approach infeasible in most applications. Monte Carlo methods can be utilized, but despite many remarkable developments in model selection methodology, generic approaches continue to be ill-suited for such high-dimensional problems. Here we develop specialized solutions for CHMMs with weak inter-chain dependencies. Specifically we construct effective proposal distributions for the hidden state process that remain computationally viable as the number of chains increases, and that require little user input or tuning. This methodology is particularly applicable to individual-level infectious disease models characterized as CHMMs, in which each chain represents an individual, and the coupling represents contact between individuals. Since the only significant contacts are between susceptible and infectious individuals, and since multiple infection pathways are often possible, the resulting CHMMs naturally have low inter-chain dependencies. We demonstrate the utility of our methodology with an application to a study of highly pathogenic avian influenza in chickens.