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

Greg M Allenby

Journal of Business & Economic Statistics, 1990, vol. 8, issue 2, 171-78

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.

Date: 1990
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