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Choice of Summary Statistic Weights in Approximate Bayesian Computation

Author

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  • Jung Hsuan

    (University of Southern California)

  • Marjoram Paul

    (University of Southern California)

Abstract

In this paper, we develop a Genetic Algorithm that can address the fundamental problem of how one should weight the summary statistics included in an approximate Bayesian computation analysis built around an accept/reject algorithm, and how one might choose the tolerance for that analysis. We then demonstrate that using weighted statistics, and a well-chosen tolerance, in such an approximate Bayesian computation approach can result in improved performance, when compared to unweighted analyses, using one example drawn purely from statistics and two drawn from the estimation of population genetics parameters.

Suggested Citation

  • Jung Hsuan & Marjoram Paul, 2011. "Choice of Summary Statistic Weights in Approximate Bayesian Computation," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 10(1), pages 1-23, September.
    • Handle: RePEc:bpj:sagmbi:v:10:y:2011:i:1:n:45
    DOI: 10.2202/1544-6115.1586
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    References listed on IDEAS

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    1. Bortot, P. & Coles, S.G. & Sisson, S.A., 2007. "Inference for Stereological Extremes," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 84-92, March.
    2. 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.
    3. 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.
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    Cited by:

    1. Soubeyrand, Samuel & Haon-Lasportes, Emilie, 2015. "Weak convergence of posteriors conditional on maximum pseudo-likelihood estimates and implications in ABC," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 84-92.
    2. Soubeyrand Samuel & Guiton François & Klein Etienne K. & Carpentier Florence, 2013. "Approximate Bayesian computation with functional statistics," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 12(1), pages 17-37, March.
    3. 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.

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