Importance sampling for partially observed temporal epidemic models

TL;DR

This paper introduces an importance sampling algorithm for Markovian epidemic models that exactly matches observed event counts, enabling efficient Bayesian inference through particle filtering and significant computational speed-ups.

Contribution

The paper presents a general importance sampling method for partially observed Markovian epidemic models, improving efficiency in Bayesian inference.

Findings

Significant speed-up in particle filtering efficiency.

Applicable to any discrete-state continuous-time Markov chain.

Exact matching of observed event counts over time.

Abstract

We present an importance sampling algorithm that can produce realisations of Markovian epidemic models that exactly match observations, taken to be the number of a single event type over a period of time. The importance sampling can be used to construct an efficient particle filter that targets the states of a system and hence estimate the likelihood to perform Bayesian parameter inference. When used in a particle marginal Metropolis Hastings scheme, the importance sampling provides a large speed-up in terms of the effective sample size per unit of computational time, compared to simple bootstrap sampling. The algorithm is general, with minimal restrictions, and we show how it can be applied to any discrete-state continuous-time Markov chain where we wish to exactly match the number of a single event type over a period of time.