Exact Inference for Stochastic Epidemic Models via Uniformly Ergodic Block Sampling

TL;DR

This paper introduces a novel, exact Bayesian inference method for stochastic SIR epidemic models using a data-augmented MCMC algorithm that efficiently explores high-dimensional latent spaces and scales to large outbreaks.

Contribution

It presents a new MCMC algorithm with a surrogate process for exact inference in stochastic epidemic models, ensuring uniform ergodicity and scalability.

Findings

Algorithm performs well in simulations

Validates with Ebola outbreak case study

Scales to large populations

Abstract

Stochastic epidemic models provide an interpretable probabilistic description of the spread of a disease through a population. Yet, fitting these models to partially observed data is a notoriously difficult task due to intractability of the likelihood for many classical models. To remedy this issue, this article introduces a novel data-augmented MCMC algorithm for exact Bayesian inference under the stochastic SIR model, given only discretely observed counts of infection. In a Metropolis-Hastings step, the latent data are jointly proposed from a surrogate process carefully designed to closely resemble the SIR model, from which we can efficiently generate epidemics consistent with the observed data. This yields a method that explores the high-dimensional latent space efficiently, and scales to outbreaks with hundreds of thousands of individuals. We show that the Markov chain underlying the algorithm is uniformly ergodic, and validate its performance via thorough simulation experiments and a case study on the 2013-2015 outbreak of Ebola Haemorrhagic Fever in Western Africa.