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Simulation-based Bayesian inference for epidemic models

Author

Listed:
  • McKinley, Trevelyan J.
  • Ross, Joshua V.
  • Deardon, Rob
  • Cook, Alex R.

Abstract

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.

Suggested Citation

  • McKinley, Trevelyan J. & Ross, Joshua V. & Deardon, Rob & Cook, Alex R., 2014. "Simulation-based Bayesian inference for epidemic models," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 434-447.
  • Handle: RePEc:eee:csdana:v:71:y:2014:i:c:p:434-447
    DOI: 10.1016/j.csda.2012.12.012
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    References listed on IDEAS

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    Cited by:

    1. Xiang, Fei & Neal, Peter, 2014. "Efficient MCMC for temporal epidemics via parameter reduction," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 240-250.
    2. Xing Ju Lee & Christopher C. Drovandi & Anthony N. Pettitt, 2015. "Model choice problems using approximate Bayesian computation with applications to pathogen transmission data sets," Biometrics, The International Biometric Society, vol. 71(1), pages 198-207, March.
    3. Peter Neal & Chien Lin Terry Huang, 2015. "Forward Simulation Markov Chain Monte Carlo with Applications to Stochastic Epidemic Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(2), pages 378-396, June.

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