A bayesian nonparametric approach for the two-sample problem
![Thumbnail](/bitstream/handle/ufscar/11579/Versao_Final_Autorizada.pdf.jpg?sequence=7&isAllowed=y)
View/ Open
Date
2018-11-19Author
Console, Rafael de Carvalho Ceregatti de
Metadata
Show full item recordAbstract
In this work, we discuss the so-called two-sample problem (PEARSON; NEYMAN, 1930)
assuming a nonparametric Bayesian approach. Considering X 1 ,...,X n and Y 1 ,...,Y m two inde-
pendent i.i.d samples generated from P 1 and P 2 , respectively, the two-sample problem consists
in deciding if P 1 and P 2 are equal. Assuming a nonparametric prior, we propose an evidence
index for the null hypothesis H 0 : P 1 = P 2 based on the posterior distribution of the distance
d(P 1 ,P 2 ) between P 1 and P 2 . 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 to 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.