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Inference in Epidemic Models without Likelihoods

Author

Listed:
  • McKinley Trevelyan

    (University of Cambridge)

  • Cook Alex R

    (National University of Singapore)

  • Deardon Robert

    (University of Guelph)

Abstract

Likelihood-based inference for epidemic models can be challenging, in part due to difficulties in evaluating the likelihood. The problem is particularly acute in models of large-scale outbreaks, and unobserved or partially observed data further complicates this process. Here we investigate the performance of Markov Chain Monte Carlo and Sequential Monte Carlo algorithms for parameter inference, where the routines are based on approximate likelihoods generated from model simulations. We compare our results to a gold-standard data-augmented MCMC for both complete and incomplete data. We illustrate our techniques using simulated epidemics as well as data from a recent outbreak of Ebola Haemorrhagic Fever in the Democratic Republic of Congo and discuss situations in which we think simulation-based inference may be preferable to likelihood-based inference.

Suggested Citation

  • 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.
  • Handle: RePEc:bpj:ijbist:v:5:y:2009:i:1:n:24
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    References listed on IDEAS

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    1. 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.
    2. Carol Y. Lin, 2008. "Modeling Infectious Diseases in Humans and Animals by KEELING, M. J. and ROHANI, P," Biometrics, The International Biometric Society, vol. 64(3), pages 993-993, September.
    3. Phenyo E. Lekone & Bärbel F. Finkenstädt, 2006. "Statistical Inference in a Stochastic Epidemic SEIR Model with Control Intervention: Ebola as a Case Study," Biometrics, The International Biometric Society, vol. 62(4), pages 1170-1177, December.
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    Citations

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    Cited by:

    1. Peters, G.W. & Sisson, S.A. & Fan, Y., 2012. "Likelihood-free Bayesian inference for α-stable models," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3743-3756.
    2. Marín Díazaraque, Juan Miguel & Rodríguez-Bernal, M. T. & Romero, E., 2016. "ABC and Hamiltonian Monte-Carlo methods in COGARCH models," DES - Working Papers. Statistics and Econometrics. WS ws1601, Universidad Carlos III de Madrid. Departamento de Estadística.
    3. repec:dau:papers:123456789/5724 is not listed on IDEAS
    4. Ajay Jasra, 2015. "Approximate Bayesian Computation for a Class of Time Series Models," International Statistical Review, International Statistical Institute, vol. 83(3), pages 405-435, December.
    5. repec:bla:jorssc:v:66:y:2017:i:4:p:717-740 is not listed on IDEAS
    6. 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.
    7. Thomas A. Dean & Sumeetpal S. Singh & Ajay Jasra & Gareth W. Peters, 2014. "Parameter Estimation for Hidden Markov Models with Intractable Likelihoods," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 970-987, December.
    8. Christian P. Robert, 2013. "Bayesian Computational Tools," Working Papers 2013-45, Center for Research in Economics and Statistics.
    9. 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.
    10. repec:bla:biomet:v:73:y:2017:i:1:p:283-293 is not listed on IDEAS

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