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Weak convergence of posteriors conditional on maximum pseudo-likelihood estimates and implications in ABC

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  • Soubeyrand, Samuel
  • Haon-Lasportes, Emilie

Abstract

The weak convergence of posterior distributions conditional on maximum pseudo-likelihood estimates (MPLE) is studied and exploited to justify the use of MPLE as summary statistics in approximate Bayesian computation (ABC). Our study could be generalized by replacing the pseudo-likelihood by other estimating functions (e.g. quasi-likelihoods and contrasts).

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:107:y:2015:i:c:p:84-92
    DOI: 10.1016/j.spl.2015.08.003
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    References listed on IDEAS

    as
    1. Soubeyrand Samuel & Carpentier Florence & Guiton François & Klein Etienne K., 2013. "Approximate Bayesian computation with functional statistics," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 12(1), pages 17-37, 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. 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.
    4. repec:dau:papers:123456789/5724 is not listed on IDEAS
    5. 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.
    6. 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.
    7. 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.
    8. Christopher C. Drovandi & Anthony N. Pettitt & Malcolm J. Faddy, 2011. "Approximate Bayesian computation using indirect inference," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 60(3), pages 317-337, May.
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    Cited by:

    1. Soyoung Kim & Jae-Kwang Kim & Kwang Woo Ahn, 2022. "A calibrated Bayesian method for the stratified proportional hazards model with missing covariates," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 28(2), pages 169-193, April.
    2. J. K. Kim & S. Yang, 2017. "A note on multiple imputation under complex sampling," Biometrika, Biometrika Trust, vol. 104(1), pages 221-228.

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