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Importance sampling for partially observed temporal epidemic models

  • Andrew J. Black
Article
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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 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 continuous-time Markov chain where we wish to exactly match the number of a single event type over a period of time.

Keywords

Importance sampling Markov chain Epidemic modelling Particle filter 

Notes

Acknowledgements

This research was supported by an ARC DECRA fellowship (DE160100690). AJB also acknowledges support from both the ARC Centre of Excellence for Mathematical and Statistical Frontiers (CoE ACEMS), and the Australian Government NHMRC Centre for Research Excellence in Policy Relevant Infectious diseases Simulation and Mathematical Modelling (CRE PRISM\(^2\)). Supercomputing resources were provided by the Phoenix HPC service at the University of Adelaide. AJB would also like to thank Joshua Ross and James Walker for comments on an earlier draft of the manuscript.

Supplementary material

11222_2018_9827_MOESM1_ESM.pdf (72 kb)
Supplementary material 1 (pdf 72 KB)

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity of AdelaideAdelaideAustralia
  2. 2.ACEMS, School of Mathematical SciencesUniversity of AdelaideAdelaideAustralia

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