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Semi-automatic selection of summary statistics for ABC model choice

Author

Listed:
  • Prangle Dennis
  • Fearnhead Paul

    (Department of Mathematics and Statistics, Lancaster University, UK)

  • Cox Murray P.
  • Biggs Patrick J.

    (Allan Wilson Centre for Molecular Ecology and Evolution, Massey University, Palmerston North, New Zealand)

  • French Nigel P.

Abstract

A central statistical goal is to choose between alternative explanatory models of data. In many modern applications, such as population genetics, it is not possible to apply standard methods based on evaluating the likelihood functions of the models, as these are numerically intractable. Approximate Bayesian computation (ABC) is a commonly used alternative for such situations. ABC simulates data x for many parameter values under each model, which is compared to the observed data xobs. More weight is placed on models under which S(x) is close to S(xobs), where S maps data to a vector of summary statistics. Previous work has shown the choice of S is crucial to the efficiency and accuracy of ABC. This paper provides a method to select good summary statistics for model choice. It uses a preliminary step, simulating many x values from all models and fitting regressions to this with the model as response. The resulting model weight estimators are used as S in an ABC analysis. Theoretical results are given to justify this as approximating low dimensional sufficient statistics. A substantive application is presented: choosing between competing coalescent models of demographic growth for Campylobacter jejuni in New Zealand using multi-locus sequence typing data.

Suggested Citation

  • Prangle Dennis & Fearnhead Paul & Cox Murray P. & Biggs Patrick J. & French Nigel P., 2014. "Semi-automatic selection of summary statistics for ABC model choice," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 13(1), pages 67-82, February.
    • Handle: RePEc:bpj:sagmbi:v:13:y:2014:i:1:p:67-82:n:5
    DOI: 10.1515/sagmb-2013-0012
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    References listed on IDEAS

    as
    1. C. C. Drovandi & A. N. Pettitt, 2011. "Estimation of Parameters for Macroparasite Population Evolution Using Approximate Bayesian Computation," Biometrics, The International Biometric Society, vol. 67(1), pages 225-233, March.
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    3. 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.
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    5. 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, June.
    6. Blum, Michael G. B., 2010. "Approximate Bayesian Computation: A Nonparametric Perspective," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1178-1187.
    7. Joyce Paul & Marjoram Paul, 2008. "Approximately Sufficient Statistics and Bayesian Computation," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 7(1), pages 1-18, August.
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    Cited by:

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    2. Michael Stocks & Mathieu Siol & Martin Lascoux & Stéphane De Mita, 2014. "Amount of Information Needed for Model Choice in Approximate Bayesian Computation," PLOS ONE, Public Library of Science, vol. 9(6), pages 1-13, June.
    3. Pierre-Olivier Goffard & Patrick Laub, 2021. "Approximate Bayesian Computations to fit and compare insurance loss models," Working Papers hal-02891046, HAL.
    4. Goffard, Pierre-Olivier & Laub, Patrick J., 2021. "Approximate Bayesian Computations to fit and compare insurance loss models," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 350-371.
    5. Lee, Xing Ju & Hainy, Markus & McKeone, James P. & Drovandi, Christopher C. & Pettitt, Anthony N., 2018. "ABC model selection for spatial extremes models applied to South Australian maximum temperature data," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 128-144.

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