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Cross-Validation, the Bayes Theorem, and Small-Sample Bias

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  • Allenby, Greg M

Abstract

Researchers in many fields of business are beginning to use cross-validatory techniques to choose between alternative models. In marketing, a Bayesian interpretation of the technique has been proposed. This article examines the Bayesian link in more detail and shows that cross-validatory posterior odds exhibit a systematic departure from exact posterior odds when sample-splitting procedures are employed. Resampling procedures also exhibit a systematic departure when the dimensions of the models differ. Methods of overcoming these biases are proposed.

Suggested Citation

  • Allenby, Greg M, 1990. "Cross-Validation, the Bayes Theorem, and Small-Sample Bias," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(2), pages 171-178, April.
    • Handle: RePEc:bes:jnlbes:v:8:y:1990:i:2:p:171-78
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    Cited by:

    1. Peter Ebbes & Dominik Papies & Harald J. van Heerde, 2011. "The Sense and Non-Sense of Holdout Sample Validation in the Presence of Endogeneity," Marketing Science, INFORMS, vol. 30(6), pages 1115-1122, November.

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