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The Effective Sample Size

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  • James Berger
  • M. J. Bayarri
  • L. R. Pericchi

Abstract

Model selection procedures often depend explicitly on the sample size n of the experiment. One example is the Bayesian information criterion (BIC) criterion and another is the use of Zellner--Siow priors in Bayesian model selection. Sample size is well-defined if one has i.i.d real observations, but is not well-defined for vector observations or in non-i.i.d. settings; extensions of critera such as BIC to such settings thus requires a definition of effective sample size that applies also in such cases. A definition of effective sample size that applies to fairly general linear models is proposed and illustrated in a variety of situations. The definition is also used to propose a suitable 'scale' for default proper priors for Bayesian model selection.

Suggested Citation

  • James Berger & M. J. Bayarri & L. R. Pericchi, 2014. "The Effective Sample Size," Econometric Reviews, Taylor & Francis Journals, vol. 33(1-4), pages 197-217, June.
    • Handle: RePEc:taf:emetrv:v:33:y:2014:i:1-4:p:197-217
    DOI: 10.1080/07474938.2013.807157
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    References listed on IDEAS

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    1. David Findley, 1991. "Counterexamples to parsimony and BIC," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(3), pages 505-514, September.
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    3. Liang, Feng & Paulo, Rui & Molina, German & Clyde, Merlise A. & Berger, Jim O., 2008. "Mixtures of g Priors for Bayesian Variable Selection," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 410-423, March.
    4. M.J. Bayarri & Gonzalo García-Donato, 2007. "Extending conventional priors for testing general hypotheses in linear models," Biometrika, Biometrika Trust, vol. 94(1), pages 135-152.
    5. Satoshi Morita & Peter F. Thall & Peter Müller, 2008. "Determining the Effective Sample Size of a Parametric Prior," Biometrics, The International Biometric Society, vol. 64(2), pages 595-602, June.
    6. David L. Weakliem, 1999. "A Critique of the Bayesian Information Criterion for Model Selection," Sociological Methods & Research, , vol. 27(3), pages 359-397, February.
    7. West, Mike, 1988. "Bayesian statistics two: Proceedings of the second Valencia international meeting on Bayesian statistics : J.M. Bernardo, M.H. DeGroot, D.V. Lindley and A.F.M. Smith (eds.), 6-10 September, 1983 (Nort," International Journal of Forecasting, Elsevier, vol. 4(4), pages 609-611.
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    Cited by:

    1. Matthew Reimherr & Xiao‐Li Meng & Dan L. Nicolae, 2021. "Prior sample size extensions for assessing prior impact and prior‐likelihood discordance," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(3), pages 413-437, July.
    2. Acosta, Jonathan & Alegría, Alfredo & Osorio, Felipe & Vallejos, Ronny, 2021. "Assessing the effective sample size for large spatial datasets: A block likelihood approach," Computational Statistics & Data Analysis, Elsevier, vol. 162(C).
    3. Gonzalo García-Donato & María Eugenia Castellanos & Alicia Quirós, 2021. "Bayesian Variable Selection with Applications in Health Sciences," Mathematics, MDPI, vol. 9(3), pages 1-16, January.
    4. Pérez, María-Eglée & Pericchi, Luis Raúl, 2014. "Changing statistical significance with the amount of information: The adaptive α significance level," Statistics & Probability Letters, Elsevier, vol. 85(C), pages 20-24.

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