A Bayesian nonparametric approach for the two-sample problem - Console, Rafael de Carvalho Ceregatti de (2018)
In this work, we discuss the so-called two-sample problem Pearson and Neyman (1930) assuming a nonparametric Bayesian approach. Considering X1; : : : ; Xn and Y1; : : : ; Ym two independent i.i.d samples generated from P1 and P2, respectively, the two-sample problem consists in deciding if P1 and P2 are equal. Assuming a nonparametric prior, we propose an evidence index for the null hypothesis H0 : P1 = P2 based on the posterior distribution of the distance d (P1; P2) between P1 and P2. This evidence index has easy computation, intuitive interpretation and can also be justified in the Bayesian decision-theoretic context. Further, in a Monte Carlo simulation study, our method presented good performance when compared with the well known Kolmogorov- Smirnov test, the Wilcoxon test as well as a recent testing procedure based on Polya tree process proposed by Holmes (HOLMES et al., 2015). Finally, we applied our method to a data set about scale measurements of three different groups of patients submitted to a questionnaire for Alzheimer\'s disease diagnostic.