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

Rafael Carvalho Ceregatti (), Rafael Izbicki () and Luis Ernesto Bueno Salasar ()
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Rafael Carvalho Ceregatti: Federal University of São Carlos
Rafael Izbicki: Federal University of São Carlos
Luis Ernesto Bueno Salasar: Federal University of São Carlos

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2021, vol. 30, issue 1, No 16, 274-291

Abstract: 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 $$P_1$$ P 1 and $$P_2$$ P 2 , which is defined by a weighted posterior expectation of the Kolmogorov–Smirnov distance between $$P_1$$ P 1 and $$P_2$$ P 2 . We present a Bayesian decision-theoretic argument to support the use of WIKS 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.

Keywords: Bayesian nonparametrics; Hypothesis testing; Two-sample problem; 62G10; 62F15 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s11749-020-00718-y

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