Efficient Bayesian Model Selection for Coupled Hidden Markov Models with Application to Infectious Diseases

• Activity Number: 58 - Advanced Bayesian Topics (Part 1)
• Type: Contributed
• Date/Time: Sunday, August 8, 2021 : 3:30 PM to 5:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Jake Carson* and Trevelyan J McKinley and Peter Neal and Simon EF Spencer
• Companies: University of Warwick and University of Exeter and University of Nottingham and University of Warwick
• Keywords: Monte Carlo; Bayes Factors; Infectious Diseases; Model Selection; Hidden Markov Models; Forward-Filtering Backward-Sampling

Abstract

Performing model selection for coupled hidden Markov models (CHMMs) is highly challenging, owing to the large dimension of the hidden state process. 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 increase, 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. When this contact is non-restrictive, 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.