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

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Li, Yuting I. 
Turk, Günther 
Pietzonka, Patrick 


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, Markov chain Monte Carlo 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.


Funder: Cambridge Trust

Funder: Engineering and Physical Sciences Research Council; Id:


Mathematics, Research articles, Bayesian inference, epidemiology, COVID-19

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Royal Society Open Science

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The Royal Society
Royal Society (RP17002)
H2020 European Research Council (740269)
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