A Bayesian Wilcoxon signed-rank test based on the Dirichlet process

Alessio Benavoli, Giorgio Corani, Francesca Mangili, Marco Zaffalon, Fabrizio Ruggeri

Abstract: Bayesian methods are ubiquitous in machine learning. Nevertheless, the analysis of empirical results is typically performed by frequentist tests. This implies dealing with null hypothesis significance tests and p-values, even though the shortcomings of such methods are well known. We propose a nonparametric Bayesian version of the Wilcoxon signed-rank test using a Dirichlet process (DP) based prior. We address in two different ways the problem of how to choose the infinite dimensional parameter that characterizes the DP. The proposed test has all the traditional strengths of the Bayesian approach; for instance, unlike the frequentist tests, it allows verifying the null hypothesis, not only rejecting it, and taking decision which minimize the expected loss. Moreover, one of the solutions proposed to model the infinitedimensional parameter of the DP, allows isolating instances in which the traditional frequentist test is guessing at random. We show results dealing with the comparison of two classifiers using real and simulated data.