Bayesian Kernel Two-Sample Testing. Issue 4 (2nd October 2022)

• Record Type: Journal Article
• Authors: Zhang, Qinyi; Wild, Veit; Filippi, Sarah; Flaxman, Seth; Sejdinovic, Dino
• Is Part Of: Journal of computational and graphical statistics. Volume 31:Issue 4(2022)
• Page Start: 1164
• Page End: 1176
• Publication Date: 2022-10-02
• Subjects: Bayes factor: Hypothesis testing -- Kernel mean embeddings; Mathematical statistics -- Data processing -- Periodicals; Mathematical statistics -- Graphic methods -- Periodicals; 519.50285
• DOI: 10.1080/10618600.2022.2067547
• Languages: English
• ISSNs: 1061-8600

Abstract

Abstract: In modern data analysis, nonparametric measures of discrepancies between random variables are particularly important. The subject is well-studied in the frequentist literature, while the development in the Bayesian setting is limited where applications are often restricted to univariate cases. Here, we propose a Bayesian kernel two-sample testing procedure based on modeling the difference between kernel mean embeddings in the reproducing kernel Hilbert space using the framework established by Flaxman et al. The use of kernel methods enables its application to random variables in generic domains beyond the multivariate Euclidean spaces. The proposed procedure results in a posterior inference scheme that allows an automatic selection of the kernel parameters relevant to the problem at hand. In a series of synthetic experiments and two real data experiments (i.e., testing network heterogeneity from high-dimensional data and six-membered monocyclic ring conformation comparison), we illustrate the advantages of our approach. Supplementary materials for this article are available online.