A bayesian nonparametric approach for the two-sample problem

• Ano de defesa: 2018
• Autor(a) principal: Console, Rafael de Carvalho Ceregatti de
• Orientador(a): Salasar, Luis Ernesto Bueno
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Universidade Federal de São Carlos; Câmpus São Carlos
• Programa de Pós-Graduação: Programa Interinstitucional de Pós-Graduação em Estatística - PIPGEs
• Palavras-chave em Português: Bayesiano não-paramétrico; Processo de Dirichlet; Teste de hipótese; Problema de duas amostras
• Palavras-chave em Inglês: Bayesian nonparametrics; Dirichlet process prior; Hypothesis testing; Two-sample problem
• Área do conhecimento CNPq: CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::INFERENCIA NAO-PARAMETRICA
• Link de acesso: https://repositorio.ufscar.br/handle/ufscar/11579

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.