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

• Rafael de Carvalho Ceregatti ^[1] ; Rafael Izbicki ^[1] ; Luis Ernesto Bueno Salasar ^[1]
  1. [1] Universidade Federal de São Carlos

     Universidade Federal de São Carlos

     Brasil

     
• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 30, Nº. 1, 2021, págs. 274-291
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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 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.