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Sequential Bayesian inference in hidden Markov stochastic kinetic models with application to detection and response to seasonal epidemics

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Abstract

We study sequential Bayesian inference in stochastic kinetic models with latent factors. Assuming continuous observation of all the reactions, our focus is on joint inference of the unknown reaction rates and the dynamic latent states, modeled as a hidden Markov factor. Using insights from nonlinear filtering of continuous-time jump Markov processes we develop a novel sequential Monte Carlo algorithm for this purpose. Our approach applies the ideas of particle learning to minimize particle degeneracy and exploit the analytical jump Markov structure. A motivating application of our methods is modeling of seasonal infectious disease outbreaks represented through a compartmental epidemic model. We demonstrate inference in such models with several numerical illustrations and also discuss predictive analysis of epidemic countermeasures using sequential Bayes estimates.

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Notes

  1. The usual H3N1 strain was also present that year and hence the time series effectively combines two distinct outbreaks.

  2. As stated by Grassly and Fraser (2006) “despite the near ubiquity of this phenomenon [seasonality], the causes and consequences of seasonal patterns of incidence are poorly understood”.

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  1. Department of Statistics & Applied Probability, UC Santa Barbara, Santa Barbara, California, USA

    Junjing Lin & Michael Ludkovski

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  1. Junjing Lin
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  2. Michael Ludkovski
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Correspondence to Michael Ludkovski.

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Lin, J., Ludkovski, M. Sequential Bayesian inference in hidden Markov stochastic kinetic models with application to detection and response to seasonal epidemics. Stat Comput 24, 1047–1062 (2014). https://doi.org/10.1007/s11222-013-9419-z

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  • DOI: https://doi.org/10.1007/s11222-013-9419-z

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