Accelerating Bayesian inference for stochastic epidemic models using incidence data

Golightly, Andrew; Wadkin, Laura E.; Whitaker, Sam A.; Baggaley, Andrew W.; Parker, Nick G.; Kypraios, Theodore

Abstract

We consider the case of performing Bayesian inference for stochastic epidemic compartment models, using incomplete time course data consisting of incidence counts that are either the number of new infections or removals in time intervals of fixed length. We eschew the most natural Markov jump process representation for reasons of computational efficiency, and focus on a stochastic differential equation representation. This is further approximated to give a tractable Gaussian process, that is, the linear noise approximation (LNA). Unless the observation model linking the LNA to data is both linear and Gaussian, the observed data likelihood remains intractable. It is in this setting that we consider two approaches for marginalising over the latent process: a correlated pseudo-marginal method and analytic marginalisation via a Gaussian approximation of the observation model. We compare and contrast these approaches using synthetic data before applying the best performing method to real data consisting of removal incidence of oak processionary moth nests in Richmond Park, London. Our approach further allows comparison between various competing compartment models.

Citation

Golightly, A., Wadkin, L. E., Whitaker, S. A., Baggaley, A. W., Parker, N. G., & Kypraios, T. (2023). Accelerating Bayesian inference for stochastic epidemic models using incidence data. Statistics and Computing, 33(6), Article 134. https://doi.org/10.1007/s11222-023-10311-6

• Journal Article Type: Article
• Acceptance Date: Sep 26, 2023
• Online Publication Date: Oct 12, 2023
• Publication Date: Dec 1, 2023
• Deposit Date: Nov 1, 2023
• Publicly Available Date: Nov 1, 2023
• Journal: Statistics and Computing
• Print ISSN: 0960-3174
• Electronic ISSN: 1573-1375
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 33
• Issue: 6
• Article Number: 134
• DOI: https://doi.org/10.1007/s11222-023-10311-6
• Keywords: Incidence data, Linear noise approximation, Stochastic epidemic model, Bayesian inference, Oak processionary moth
• Public URL: https://nottingham-repository.worktribe.com/output/26213670
• Publisher URL: https://link.springer.com/article/10.1007/s11222-023-10311-6
• Additional Information: Received: 27 March 2023; Accepted: 26 September 2023; First Online: 12 October 2023; : ; : The authors declare no competing interests.