WIKS: a general Bayesian nonparametric index for quantifying differences between two populations

Author(s)

Ceregatti, Rafael de Carvalho ; Izbicki, Rafael ; Bueno Salasar, Luis Ernesto

• Document type: Journal article
• Source: TEST; v. 30, n. 1, p. 18-pg., 2020-05-29.

Abstract

A key problem in many research investigations is to decide whether two samples have the same distribution. Numerous statistical methods have been devoted to this issue, but only few considered a Bayesian nonparametric approach. In this paper, we propose a novel nonparametric Bayesian index (WIKS) for quantifying the difference between two populations P1 and P2, which is defined by a weighted posterior expectation of the Kolmogorov-Smirnov distance between P1 and P2. We present a Bayesian decision-theoretic argument to support the use ofWIKS index and a simple algorithm to compute it. Furthermore, we prove that WIKS is a statistically consistent procedure and that it controls the significance level uniformly over the null hypothesis, a feature that simplifies the choice of cutoff values for taking decisions. We present a real data analysis and an extensive simulation study showing that WIKS is more powerful than competing approaches under several settings. (AU)

• FAPESP's process: 19/11321-9 - Neural networks in statistical inference problems
• Grantee: Rafael Izbicki
• Support Opportunities: Regular Research Grants
• FAPESP's process: 17/03363-8 - Interpretability and efficiency in hypothesis tests
• Grantee: Rafael Izbicki
• Support Opportunities: Regular Research Grants