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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
    DOI: 10.2202/1557-4679.1171
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    References listed on IDEAS

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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. Henri Pesonen & Umberto Simola & Alvaro Köhn‐Luque & Henri Vuollekoski & Xiaoran Lai & Arnoldo Frigessi & Samuel Kaski & David T. Frazier & Worapree Maneesoonthorn & Gael M. Martin & Jukka Corander, 2023. "ABC of the future," International Statistical Review, International Statistical Institute, vol. 91(2), pages 243-268, August.
    3. Filippi Sarah & Barnes Chris P. & Cornebise Julien & Stumpf Michael P.H., 2013. "On optimality of kernels for approximate Bayesian computation using sequential Monte Carlo," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 12(1), pages 87-107, March.
    4. 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.
    5. I. Andrianakis & I. Vernon & N. McCreesh & T. J. McKinley & J. E. Oakley & R. N. Nsubuga & M. Goldstein & R. G. White, 2017. "History matching of a complex epidemiological model of human immunodeficiency virus transmission by using variance emulation," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(4), pages 717-740, August.
    6. Ioannis Andrianakis & Ian R Vernon & Nicky McCreesh & Trevelyan J McKinley & Jeremy E Oakley & Rebecca N Nsubuga & Michael Goldstein & Richard G White, 2015. "Bayesian History Matching of Complex Infectious Disease Models Using Emulation: A Tutorial and a Case Study on HIV in Uganda," PLOS Computational Biology, Public Library of Science, vol. 11(1), pages 1-18, January.
    7. 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.
    8. 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.
    9. Nunes Matthew A & Balding David J, 2010. "On Optimal Selection of Summary Statistics for Approximate Bayesian Computation," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 9(1), pages 1-16, September.
    10. Christian P. Robert, 2013. "Bayesian Computational Tools," Working Papers 2013-45, Center for Research in Economics and Statistics.
    11. 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.
    12. repec:dau:papers:123456789/5724 is not listed on IDEAS
    13. Bertl Johanna & Ewing Gregory & Kosiol Carolin & Futschik Andreas, 2017. "Approximate maximum likelihood estimation for population genetic inference," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 16(5-6), pages 291-312, December.
    14. Cici Bauer & Jon Wakefield, 2018. "Stratified space–time infectious disease modelling, with an application to hand, foot and mouth disease in China," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 67(5), pages 1379-1398, November.
    15. Leigh Fisher & Jon Wakefield & Cici Bauer & Steve Self, 2017. "Time series modeling of pathogen-specific disease probabilities with subsampled data," Biometrics, The International Biometric Society, vol. 73(1), pages 283-293, March.
    16. repec:bla:istatr:v:83:y:2015:i:3:p:405-435 is not listed on IDEAS
    17. Jonathan U Harrison & Ruth E Baker, 2020. "An automatic adaptive method to combine summary statistics in approximate Bayesian computation," PLOS ONE, Public Library of Science, vol. 15(8), pages 1-21, August.
    18. Andrew J K Conlan & Trevelyan J McKinley & Katerina Karolemeas & Ellen Brooks Pollock & Anthony V Goodchild & Andrew P Mitchell & Colin P D Birch & Richard S Clifton-Hadley & James L N Wood, 2012. "Estimating the Hidden Burden of Bovine Tuberculosis in Great Britain," PLOS Computational Biology, Public Library of Science, vol. 8(10), pages 1-14, October.
    19. Elena Ehrlich & Ajay Jasra & Nikolas Kantas, 2015. "Gradient Free Parameter Estimation for Hidden Markov Models with Intractable Likelihoods," Methodology and Computing in Applied Probability, Springer, vol. 17(2), pages 315-349, June.

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