Efficient Bayesian inference of fully stochastic epidemiological models with applications to COVID-19

TL;DR

This paper introduces an efficient Bayesian inference method for stochastic epidemiological models, enabling uncertainty quantification and parameter estimation in large populations, demonstrated on early COVID-19 data in the UK.

Contribution

The paper develops a novel likelihood approximation for non-stationary Markov models, improving computational efficiency for Bayesian inference in epidemiology.

Findings

Successfully analyzed early COVID-19 UK data

Provided MAP estimates and posterior sampling

Quantified parameter sensitivities using Fisher information

Abstract

Epidemiological forecasts are beset by uncertainties about the underlying epidemiological processes, and the surveillance process through which data are acquired. We present a Bayesian inference methodology that quantifies these uncertainties, for epidemics that are modelled by (possibly) non-stationary, continuous-time, Markov population processes. The efficiency of the method derives from a functional central limit theorem approximation of the likelihood, valid for large populations. We demonstrate the methodology by analysing the early stages of the COVID-19 pandemic in the UK, based on age-structured data for the number of deaths. This includes maximum a posteriori estimates, MCMC sampling of the posterior, computation of the model evidence, and the determination of parameter sensitivities via the Fisher information matrix. Our methodology is implemented in PyRoss, an open-source platform for analysis of epidemiological compartment models.