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

Author

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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)

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.

Suggested Citation

  • Rafael Carvalho Ceregatti & Rafael Izbicki & Luis Ernesto Bueno Salasar, 2021. "WIKS: a general Bayesian nonparametric index for quantifying differences between two populations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 274-291, March.
    • Handle: RePEc:spr:testjl:v:30:y:2021:i:1:d:10.1007_s11749-020-00718-y
    DOI: 10.1007/s11749-020-00718-y
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