Simulation-based Bayesian inference for epidemic models
A powerful and flexible method for fitting dynamic models to missing and censored data is to use the Bayesian paradigm via data-augmented Markov chain Monte Carlo (DA-MCMC). This samples from the joint posterior for the parameters and missing data, but requires high memory overheads for large-scale systems. In addition, designing efficient proposal distributions for the missing data is typically challenging. Pseudo-marginal methods instead integrate across the missing data using a Monte Carlo estimate for the likelihood, generated from multiple independent simulations from the model. These techniques can avoid the high memory requirements of DA-MCMC, and under certain conditions produce the exact marginal posterior distribution for parameters. A novel method is presented for implementing importance sampling for dynamic epidemic models, by conditioning the simulations on sets of validity criteria (based on the model structure) as well as the observed data. The flexibility of these techniques is illustrated using both removal time and final size data from an outbreak of smallpox. It is shown that these approaches can circumvent the need for reversible-jump MCMC, and can allow inference in situations where DA-MCMC is impossible due to computationally infeasible likelihoods.
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- Wierman, John C. & Marchette, David J., 2004. "Modeling computer virus prevalence with a susceptible-infected-susceptible model with reintroduction," Computational Statistics & Data Analysis, Elsevier, vol. 45(1), pages 3-23, February.
- Paul Fearnhead & Loukia Meligkotsidou, 2004. "Exact filtering for partially observed continuous time models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(3), pages 771-789.
- Nikolaos Demiris & Philip D. O'Neill, 2005. "Bayesian inference for epidemics with two levels of mixing," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(2), pages 265-280.
- Philip D. O'Neill & David J. Balding & Niels G. Becker & Mervi Eerola & Denis Mollison, 2000. "Analyses of infectious disease data from household outbreaks by Markov chain Monte Carlo methods," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 49(4), pages 517-542.
- Erhardt, Robert J. & Smith, Richard L., 2012. "Approximate Bayesian computing for spatial extremes," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1468-1481.
- Mark A. Beaumont & Jean-Marie Cornuet & Jean-Michel Marin & Christian P. Robert, 2009. "Adaptive approximate Bayesian computation," Biometrika, Biometrika Trust, vol. 96(4), pages 983-990.
- Paul Fearnhead & Dennis Prangle, 2012. "Constructing summary statistics for approximate Bayesian computation: semi-automatic approximate Bayesian computation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(3), pages 419-474, 06.
- Wong, Heung & Shao, Quanxi & Ip, Wai-cheung, 2013. "Modeling respiratory illnesses with change point: A lesson from the SARS epidemic in Hong Kong," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 589-599.
- Hohle, Michael & Feldmann, Ulrike, 2007. "RLadyBug--An R package for stochastic epidemic models," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 680-686, October.
- McKinley Trevelyan & Cook Alex R & Deardon Robert, 2009. "Inference in Epidemic Models without Likelihoods," The International Journal of Biostatistics, De Gruyter, vol. 5(1), pages 1-40, July.
- Celeux, Gilles & Marin, Jean-Michel & Robert, Christian P., 2006. "Iterated importance sampling in missing data problems," Economics Papers from University Paris Dauphine 123456789/6215, Paris Dauphine University.
- Christophe Andrieu & Arnaud Doucet & Roman Holenstein, 2010. "Particle Markov chain Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 269-342.
- Celeux, Gilles & Marin, Jean-Michel & Robert, Christian P., 2006. "Iterated importance sampling in missing data problems," Computational Statistics & Data Analysis, Elsevier, vol. 50(12), pages 3386-3404, August.
- P. D. O'Neill & G. O. Roberts, 1999. "Bayesian inference for partially observed stochastic epidemics," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 162(1), pages 121-129.
- Cappé, Olivier & Guillin, Arnaud & Marin, Jean-Michel & Robert, Christian P., 2004. "Population Monte Carlo," Economics Papers from University Paris Dauphine 123456789/6072, Paris Dauphine University.
- Yang, Yang & Longini Jr., Ira M. & Elizabeth Halloran, M., 2007. "A data-augmentation method for infectious disease incidence data from close contact groups," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6582-6595, August.
- Nikolaos Demiris & Philip D. O'Neill, 2005. "Bayesian inference for stochastic multitype epidemics in structured populations via random graphs," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 731-745.
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