Bayesian Tests for Checking the Equality of Distributions, with Application to Screening Variables for Classification

Abstract

A new framework for nonparametrically testing of equality of two densities is proposed. From this framework, two different tests are constructed. The two tests themselves are then investigated and compared to other tests on simulated and real data. After establishing their legitimacy, the tests are applied to choose variables for classification problems. We study the benefit of these tests, when they are useful and what classification techniques work best in conjunction with them. The method is then applied to simulated data sets and real data sets where the number of variables is large.