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Posterior Predictive Checking for Partially Observed Stochastic Epidemic Models

Aristotelous, Georgios; Kypraios, Theodore; O'Neill, Philip D.

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Georgios Aristotelous

Philip D. O'Neill


We address the problem of assessing the fit of stochastic epidemic models to data. Two novel model assessment methods are developed, based on disease progression curves, namely the distance method and the position-time method. The methods are illustrated using SIR (susceptible-infective-removed) models. We assume a typical data observation setting in which case-detection times are observed while infection times are not. Both methods involve Bayesian posterior predic-tive checking, in which the observed data are compared to data generated from the posterior predictive distribution. The distance method does this by calculating distances between disease progression curves, while the position-time method does this pointwise at suitably selected time points. Both methods provide visual and quantitative outputs with meaningful interpretations. The performance of the methods benefits from the development and application of a time-shifting method that accounts for the random time delay until an epidemic takes off. Extensive simulation studies show that both methods can successfully be used to assess the choice of infectious period distribution and the choice of infection rate function. MSC2020 subject classifications: Primary 62F15, 62P10; secondary 62-08.


Aristotelous, G., Kypraios, T., & O'Neill, P. D. (2023). Posterior Predictive Checking for Partially Observed Stochastic Epidemic Models. Bayesian Analysis, 18(4), 1283-1310.

Journal Article Type Article
Acceptance Date Sep 13, 2022
Online Publication Date Oct 4, 2022
Publication Date 2023-12
Deposit Date Sep 29, 2022
Publicly Available Date Oct 4, 2022
Journal Bayesian Analysis
Print ISSN 1936-0975
Electronic ISSN 1931-6690
Publisher International Society for Bayesian Analysis
Peer Reviewed Peer Reviewed
Volume 18
Issue 4
Pages 1283-1310
Keywords Applied Mathematics; Statistics and Probability
Public URL
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