A bayesian nonparametric approach for the two-sample problem
Autor(a) principal: | |
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Data de Publicação: | 2018 |
Tipo de documento: | Dissertação |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFSCAR |
Texto Completo: | https://repositorio.ufscar.br/handle/ufscar/11579 |
Resumo: | 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. |
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Console, Rafael de Carvalho Ceregatti deSalasar, Luis Ernesto Buenohttp://lattes.cnpq.br/5464564215528609http://lattes.cnpq.br/5405464055196044ea80e7c7-b7ab-4912-835b-a1a67dcd3d3a2019-08-01T16:13:01Z2019-08-01T16:13:01Z2018-11-19CONSOLE, Rafael de Carvalho Ceregatti de. A bayesian nonparametric approach for the two-sample problem. 2018. Dissertação (Mestrado em Estatística) – Universidade Federal de São Carlos, São Carlos, 2018. Disponível em: https://repositorio.ufscar.br/handle/ufscar/11579.https://repositorio.ufscar.br/handle/ufscar/11579In 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.Neste trabalho, discutimos o problema conhecido como problema de duas amostras utilizando uma abordagem bayesiana não-paramétrica. Considere X 1 ,...,X n e Y 1 ,...,Y m duas amostras independentes, geradas por P1 e P2, respectivamente, o problema de duas amostras consiste em decidir se P 1 e P 2 são iguais. Assumindo uma priori não-paramétrica, propomos um índice de evidência para a hipótese nula H 0 : P 1 = P 2 baseado na distribuição a posteriori da distância d(P 1 ,P 2 ) entre P 1 e P 2 . O índice de evidência é de fácil implementação, tem uma interpretação intuitiva e também pode ser justificada no contexto da teoria da decisão bayesiana. Além disso, em um estudo de simulação de Monte Carlo, nosso método apresentou bom desempenho quando comparado com o teste de Kolmogorov-Smirnov, com o teste de Wilcoxon e com o método de Holmes. Finalmente, aplicamos nosso método em um conjunto de dados sobre medidas de escala de três grupos diferentes de pacientes submetidos a um questionário para diagnóstico de doença de Alzheimer.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)engUniversidade Federal de São CarlosCâmpus São CarlosPrograma Interinstitucional de Pós-Graduação em Estatística - PIPGEsUFSCarBayesiano não-paramétricoProcesso de DirichletTeste de hipóteseProblema de duas amostrasBayesian nonparametricsDirichlet process priorHypothesis testingTwo-sample problemCIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::INFERENCIA NAO-PARAMETRICAA bayesian nonparametric approach for the two-sample problemUma abordagem bayesiana não paramétrica para o problema de duas amostrasinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisOnline600600d18bde29-0b98-43e9-ae00-55c68009667ainfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFSCARinstname:Universidade Federal de São Carlos (UFSCAR)instacron:UFSCARORIGINALVersao_Final_Autorizada.pdfVersao_Final_Autorizada.pdfapplication/pdf1283750https://repositorio.ufscar.br/bitstream/ufscar/11579/1/Versao_Final_Autorizada.pdf9f77e5dc6d3d0ef4f584187de3676315MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81957https://repositorio.ufscar.br/bitstream/ufscar/11579/3/license.txtae0398b6f8b235e40ad82cba6c50031dMD53TEXTVersao_Final_Autorizada.pdf.txtVersao_Final_Autorizada.pdf.txtExtracted texttext/plain48994https://repositorio.ufscar.br/bitstream/ufscar/11579/4/Versao_Final_Autorizada.pdf.txtc01ec577822321c0cc33421a5efcfcb5MD54THUMBNAILVersao_Final_Autorizada.pdf.jpgVersao_Final_Autorizada.pdf.jpgIM Thumbnailimage/jpeg5827https://repositorio.ufscar.br/bitstream/ufscar/11579/5/Versao_Final_Autorizada.pdf.jpg5bdbc42ab82777979db6d5ab9e1093c0MD55ufscar/115792023-09-18 18:31:23.167oai:repositorio.ufscar.br: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Repositório InstitucionalPUBhttps://repositorio.ufscar.br/oai/requestopendoar:43222023-09-18T18:31:23Repositório Institucional da UFSCAR - Universidade Federal de São Carlos (UFSCAR)false |
dc.title.eng.fl_str_mv |
A bayesian nonparametric approach for the two-sample problem |
dc.title.alternative.por.fl_str_mv |
Uma abordagem bayesiana não paramétrica para o problema de duas amostras |
title |
A bayesian nonparametric approach for the two-sample problem |
spellingShingle |
A bayesian nonparametric approach for the two-sample problem Console, Rafael de Carvalho Ceregatti de Bayesiano não-paramétrico Processo de Dirichlet Teste de hipótese Problema de duas amostras Bayesian nonparametrics Dirichlet process prior Hypothesis testing Two-sample problem CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::INFERENCIA NAO-PARAMETRICA |
title_short |
A bayesian nonparametric approach for the two-sample problem |
title_full |
A bayesian nonparametric approach for the two-sample problem |
title_fullStr |
A bayesian nonparametric approach for the two-sample problem |
title_full_unstemmed |
A bayesian nonparametric approach for the two-sample problem |
title_sort |
A bayesian nonparametric approach for the two-sample problem |
author |
Console, Rafael de Carvalho Ceregatti de |
author_facet |
Console, Rafael de Carvalho Ceregatti de |
author_role |
author |
dc.contributor.authorlattes.por.fl_str_mv |
http://lattes.cnpq.br/5405464055196044 |
dc.contributor.author.fl_str_mv |
Console, Rafael de Carvalho Ceregatti de |
dc.contributor.advisor1.fl_str_mv |
Salasar, Luis Ernesto Bueno |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/5464564215528609 |
dc.contributor.authorID.fl_str_mv |
ea80e7c7-b7ab-4912-835b-a1a67dcd3d3a |
contributor_str_mv |
Salasar, Luis Ernesto Bueno |
dc.subject.por.fl_str_mv |
Bayesiano não-paramétrico Processo de Dirichlet Teste de hipótese Problema de duas amostras |
topic |
Bayesiano não-paramétrico Processo de Dirichlet Teste de hipótese Problema de duas amostras Bayesian nonparametrics Dirichlet process prior Hypothesis testing Two-sample problem CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::INFERENCIA NAO-PARAMETRICA |
dc.subject.eng.fl_str_mv |
Bayesian nonparametrics Dirichlet process prior Hypothesis testing Two-sample problem |
dc.subject.cnpq.fl_str_mv |
CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::INFERENCIA NAO-PARAMETRICA |
description |
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. |
publishDate |
2018 |
dc.date.issued.fl_str_mv |
2018-11-19 |
dc.date.accessioned.fl_str_mv |
2019-08-01T16:13:01Z |
dc.date.available.fl_str_mv |
2019-08-01T16:13:01Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/masterThesis |
format |
masterThesis |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
CONSOLE, Rafael de Carvalho Ceregatti de. A bayesian nonparametric approach for the two-sample problem. 2018. Dissertação (Mestrado em Estatística) – Universidade Federal de São Carlos, São Carlos, 2018. Disponível em: https://repositorio.ufscar.br/handle/ufscar/11579. |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufscar.br/handle/ufscar/11579 |
identifier_str_mv |
CONSOLE, Rafael de Carvalho Ceregatti de. A bayesian nonparametric approach for the two-sample problem. 2018. Dissertação (Mestrado em Estatística) – Universidade Federal de São Carlos, São Carlos, 2018. Disponível em: https://repositorio.ufscar.br/handle/ufscar/11579. |
url |
https://repositorio.ufscar.br/handle/ufscar/11579 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.confidence.fl_str_mv |
600 600 |
dc.relation.authority.fl_str_mv |
d18bde29-0b98-43e9-ae00-55c68009667a |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Universidade Federal de São Carlos Câmpus São Carlos |
dc.publisher.program.fl_str_mv |
Programa Interinstitucional de Pós-Graduação em Estatística - PIPGEs |
dc.publisher.initials.fl_str_mv |
UFSCar |
publisher.none.fl_str_mv |
Universidade Federal de São Carlos Câmpus São Carlos |
dc.source.none.fl_str_mv |
reponame:Repositório Institucional da UFSCAR instname:Universidade Federal de São Carlos (UFSCAR) instacron:UFSCAR |
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Repositório Institucional da UFSCAR |
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