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Relevant statistics for Bayesian model choice

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  • Jean-Michel Marin
  • Natesh S. Pillai
  • Christian P. Robert
  • Judith Rousseau

Abstract

type="main" xml:id="rssb12056-abs-0001"> The choice of the summary statistics that are used in Bayesian inference and in particular in approximate Bayesian computation algorithms has bearings on the validation of the resulting inference. Those statistics are nonetheless customarily used in approximate Bayesian computation algorithms without consistency checks. We derive necessary and sufficient conditions on summary statistics for the corresponding Bayes factor to be convergent, namely to select the true model asymptotically. Those conditions, which amount to the expectations of the summary statistics differing asymptotically under the two models, are quite natural and can be exploited in approximate Bayesian computation settings to infer whether or not a choice of summary statistics is appropriate, via a Monte Carlo validation.

Suggested Citation

  • Jean-Michel Marin & Natesh S. Pillai & Christian P. Robert & Judith Rousseau, 2014. "Relevant statistics for Bayesian model choice," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(5), pages 833-859, November.
    • Handle: RePEc:bla:jorssb:v:76:y:2014:i:5:p:833-859
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    File URL: http://hdl.handle.net/10.1111/rssb.2014.76.issue-5
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    Cited by:

    1. 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.
    2. Roxana Zeraati & Yan-Liang Shi & Nicholas A. Steinmetz & Marc A. Gieselmann & Alexander Thiele & Tirin Moore & Anna Levina & Tatiana A. Engel, 2023. "Intrinsic timescales in the visual cortex change with selective attention and reflect spatial connectivity," Nature Communications, Nature, vol. 14(1), pages 1-19, December.
    3. Frazier, David T. & Maneesoonthorn, Worapree & Martin, Gael M. & McCabe, Brendan P.M., 2019. "Approximate Bayesian forecasting," International Journal of Forecasting, Elsevier, vol. 35(2), pages 521-539.
    4. Li, Cheng & Jiang, Wenxin, 2016. "On oracle property and asymptotic validity of Bayesian generalized method of moments," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 132-147.
    5. Sifat A Moon & Lee W Cohnstaedt & D Scott McVey & Caterina M Scoglio, 2019. "A spatio-temporal individual-based network framework for West Nile virus in the USA: Spreading pattern of West Nile virus," PLOS Computational Biology, Public Library of Science, vol. 15(3), pages 1-24, March.
    6. D.T. Frazier & G.M. Martin & C.P. Robert & J. Rousseau, 2016. "Asymptotic Properties of Approximate Bayesian Computation," Monash Econometrics and Business Statistics Working Papers 18/16, Monash University, Department of Econometrics and Business Statistics.
    7. Minerva Mukhopadhyay & Sourabh Bhattacharya, 2022. "Bayes factor asymptotics for variable selection in the Gaussian process framework," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(3), pages 581-613, June.
    8. 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.
    9. Kobayashi, Genya, 2014. "A transdimensional approximate Bayesian computation using the pseudo-marginal approach for model choice," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 167-183.
    10. D T Frazier & G M Martin & C P Robert & J Rousseau, 2018. "Asymptotic properties of approximate Bayesian computation," Biometrika, Biometrika Trust, vol. 105(3), pages 593-607.
    11. David T. Frazier & Gael M. Martin & Christian P. Robert, 2015. "On Consistency of Approximate Bayesian Computation," Monash Econometrics and Business Statistics Working Papers 19/15, Monash University, Department of Econometrics and Business Statistics.

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