Use of Cross-validation Bayes Factors to Test Equality of Two Densities

2020/03/13 by Jeffery Hart, Hart, Jeffery, Taeryon Choi +3
Computer Science · Mathematics · #Applications (stat.AP) #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2003.06368

openalex publication_date 2020/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose a non-parametric, two-sample Bayesian test for checking whether or not two data sets share a common distribution. The test makes use of data splitting ideas and does not require priors for high-dimensional parameter vectors as do other nonparametric Bayesian procedures. We provide evidence that the new procedure provides more stable Bayes factors than do methods based on Pólya trees. Somewhat surprisingly, the behavior of the proposed Bayes factors when the two distributions are the same is usually superior to that of Pólya tree Bayes factors. We showcase the effectiveness of the test by proving its consistency, conducting a simulation study and applying the test to Higgs boson data.

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