Bayesian variable selection for logistic mixture models with Pólya-Gamma data augmentation
Autor(a) principal: | |
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Data de Publicação: | 2022 |
Tipo de documento: | Dissertação |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFSCAR |
Texto Completo: | https://repositorio.ufscar.br/handle/ufscar/15643 |
Resumo: | In this work, Bayesian methods for estimating and selecting variables in a mixture of logistic regressions model are presented. In order to simplify its Bayesian estimation, we extend the data augmentation approach with Pólya-Gamma random variables to the mixture of logistic regression models. Through the data augmentation approach, we present a Gibbs sampling algorithm for estimating the full model, and the number of components in the mixture is identified by Bayesian model selection criteria. In the model with variable selection, we investigate the performance of two prior distributions for the regression coefficients, adding a second set of latent variables to indicate the presence and non-presence of the predictor variables at each component of the mixture. Analogously to the full model, a Gibbs sampling algorithm is applied to the model with variable selection and the conjugation obtained for the distribution of the regression coefficients, through the inclusion of Pólya-Gamma variables, allows us to analytically calculate the marginal likelihood and gain computational efficiency in the variable selection process. To analyse the performance, the presented methodologies are applied in simulated and real data. |
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Bogoni, Mariella AnaniasZuanetti, Daiane Aparecidahttp://lattes.cnpq.br/8352484284929824http://lattes.cnpq.br/1099499926393005d8729a43-9739-494e-9b1f-f24a64935c8d2022-02-23T18:24:34Z2022-02-23T18:24:34Z2022-02-15BOGONI, Mariella Ananias. Bayesian variable selection for logistic mixture models with Pólya-Gamma data augmentation. 2022. Dissertação (Mestrado em Estatística) – Universidade Federal de São Carlos, São Carlos, 2022. Disponível em: https://repositorio.ufscar.br/handle/ufscar/15643.https://repositorio.ufscar.br/handle/ufscar/15643In this work, Bayesian methods for estimating and selecting variables in a mixture of logistic regressions model are presented. In order to simplify its Bayesian estimation, we extend the data augmentation approach with Pólya-Gamma random variables to the mixture of logistic regression models. Through the data augmentation approach, we present a Gibbs sampling algorithm for estimating the full model, and the number of components in the mixture is identified by Bayesian model selection criteria. In the model with variable selection, we investigate the performance of two prior distributions for the regression coefficients, adding a second set of latent variables to indicate the presence and non-presence of the predictor variables at each component of the mixture. Analogously to the full model, a Gibbs sampling algorithm is applied to the model with variable selection and the conjugation obtained for the distribution of the regression coefficients, through the inclusion of Pólya-Gamma variables, allows us to analytically calculate the marginal likelihood and gain computational efficiency in the variable selection process. To analyse the performance, the presented methodologies are applied in simulated and real data.Neste trabalho, métodos Bayesianos para estimação e seleção de variáveis em um modelo de mistura de regressão logística são apresentados. Com o objetivo de simplificar a inferência Bayesiana e ganhar eficiência computacional, a abordagem de aumento de dados com variáveis latentes Pólya-Gama é estendida para modelos de mistura de regressão logística. Através dela, o algoritmo amostrador de Gibbs é aplicado para a estimação do modelo completo, com a estimação do número de componentes da mistura sendo feita através de critérios Bayesianos de seleção de modelos. Para a seleção de variáveis, duas distribuições a priori para os coeficientes de regressão são investigadas, adicionando um segundo conjunto de variáveis latentes para indicar a presença e ausência das variáveis preditoras em cada componente da mistura. De modo análogo ao modelo completo, o algoritmo amostrador de Gibbs é aplicado no modelo com a seleção de variáveis e a conjugação obtida para a distribuição dos coeficientes de regressão, com a inclusão das variáveis Pólya-Gama, nos permite calcular analiticamente a verossimilhança marginal e ganhar eficiência computacional no processo de seleção de variáveis. Para analisar a performance dos métodos, as metodologias apresentadas são aplicadas em dados simulados e reais.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)CAPES: Código de Financiamento 001engUniversidade Federal de São CarlosCâmpus São CarlosPrograma Interinstitucional de Pós-Graduação em Estatística - PIPGEsUFSCarAttribution-NonCommercial-NoDerivs 3.0 Brazilhttp://creativecommons.org/licenses/by-nc-nd/3.0/br/info:eu-repo/semantics/openAccessVariable selectionG-priorSpike and slab priorPólya-Gamma-samplingSeleção de variáveisG-prioriPriori spike e slabCIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICABayesian variable selection for logistic mixture models with Pólya-Gamma data augmentationSeleção Bayesiana de variáveis para modelos de mistura de regressão logística com variáveis latentes Pólya-Gammainfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesis600600b32a2fc3-5d19-41db-9bab-08a95238ddf5reponame:Repositório Institucional da UFSCARinstname:Universidade Federal de São Carlos (UFSCAR)instacron:UFSCARCC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8811https://repositorio.ufscar.br/bitstream/ufscar/15643/4/license_rdfe39d27027a6cc9cb039ad269a5db8e34MD54ORIGINALmonografia_final_ufscar.pdfmonografia_final_ufscar.pdfTexto da dissertação revisadoapplication/pdf971909https://repositorio.ufscar.br/bitstream/ufscar/15643/1/monografia_final_ufscar.pdf4e4ef31a285a48237becf1bc044c5d53MD51Modelo carta-comprovante PIPGEs.pdfModelo carta-comprovante PIPGEs.pdfCarta de autorização de depositoapplication/pdf338505https://repositorio.ufscar.br/bitstream/ufscar/15643/3/Modelo%20carta-comprovante%20PIPGEs.pdfd5c1dc03e026e43153395146cca63edfMD53TEXTmonografia_final_ufscar.pdf.txtmonografia_final_ufscar.pdf.txtExtracted texttext/plain162201https://repositorio.ufscar.br/bitstream/ufscar/15643/5/monografia_final_ufscar.pdf.txted62bbc7bb04e130c750f10bb6e404f1MD55Modelo carta-comprovante PIPGEs.pdf.txtModelo carta-comprovante PIPGEs.pdf.txtExtracted texttext/plain1368https://repositorio.ufscar.br/bitstream/ufscar/15643/7/Modelo%20carta-comprovante%20PIPGEs.pdf.txt218babd59720eb7af7112dbdec3997fbMD57THUMBNAILmonografia_final_ufscar.pdf.jpgmonografia_final_ufscar.pdf.jpgIM Thumbnailimage/jpeg15181https://repositorio.ufscar.br/bitstream/ufscar/15643/6/monografia_final_ufscar.pdf.jpgb7fcb06b399f3b25f1b0e173a91d884dMD56Modelo carta-comprovante PIPGEs.pdf.jpgModelo carta-comprovante PIPGEs.pdf.jpgIM Thumbnailimage/jpeg13124https://repositorio.ufscar.br/bitstream/ufscar/15643/8/Modelo%20carta-comprovante%20PIPGEs.pdf.jpgcde5af8cf12f248d0892c7b72ee6ac86MD58ufscar/156432023-09-18 18:32:25.672oai:repositorio.ufscar.br:ufscar/15643Repositório InstitucionalPUBhttps://repositorio.ufscar.br/oai/requestopendoar:43222023-09-18T18:32:25Repositório Institucional da UFSCAR - Universidade Federal de São Carlos (UFSCAR)false |
dc.title.eng.fl_str_mv |
Bayesian variable selection for logistic mixture models with Pólya-Gamma data augmentation |
dc.title.alternative.por.fl_str_mv |
Seleção Bayesiana de variáveis para modelos de mistura de regressão logística com variáveis latentes Pólya-Gamma |
title |
Bayesian variable selection for logistic mixture models with Pólya-Gamma data augmentation |
spellingShingle |
Bayesian variable selection for logistic mixture models with Pólya-Gamma data augmentation Bogoni, Mariella Ananias Variable selection G-prior Spike and slab prior Pólya-Gamma-sampling Seleção de variáveis G-priori Priori spike e slab CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA |
title_short |
Bayesian variable selection for logistic mixture models with Pólya-Gamma data augmentation |
title_full |
Bayesian variable selection for logistic mixture models with Pólya-Gamma data augmentation |
title_fullStr |
Bayesian variable selection for logistic mixture models with Pólya-Gamma data augmentation |
title_full_unstemmed |
Bayesian variable selection for logistic mixture models with Pólya-Gamma data augmentation |
title_sort |
Bayesian variable selection for logistic mixture models with Pólya-Gamma data augmentation |
author |
Bogoni, Mariella Ananias |
author_facet |
Bogoni, Mariella Ananias |
author_role |
author |
dc.contributor.authorlattes.por.fl_str_mv |
http://lattes.cnpq.br/1099499926393005 |
dc.contributor.author.fl_str_mv |
Bogoni, Mariella Ananias |
dc.contributor.advisor1.fl_str_mv |
Zuanetti, Daiane Aparecida |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/8352484284929824 |
dc.contributor.authorID.fl_str_mv |
d8729a43-9739-494e-9b1f-f24a64935c8d |
contributor_str_mv |
Zuanetti, Daiane Aparecida |
dc.subject.eng.fl_str_mv |
Variable selection G-prior Spike and slab prior Pólya-Gamma-sampling |
topic |
Variable selection G-prior Spike and slab prior Pólya-Gamma-sampling Seleção de variáveis G-priori Priori spike e slab CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA |
dc.subject.por.fl_str_mv |
Seleção de variáveis G-priori Priori spike e slab |
dc.subject.cnpq.fl_str_mv |
CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA |
description |
In this work, Bayesian methods for estimating and selecting variables in a mixture of logistic regressions model are presented. In order to simplify its Bayesian estimation, we extend the data augmentation approach with Pólya-Gamma random variables to the mixture of logistic regression models. Through the data augmentation approach, we present a Gibbs sampling algorithm for estimating the full model, and the number of components in the mixture is identified by Bayesian model selection criteria. In the model with variable selection, we investigate the performance of two prior distributions for the regression coefficients, adding a second set of latent variables to indicate the presence and non-presence of the predictor variables at each component of the mixture. Analogously to the full model, a Gibbs sampling algorithm is applied to the model with variable selection and the conjugation obtained for the distribution of the regression coefficients, through the inclusion of Pólya-Gamma variables, allows us to analytically calculate the marginal likelihood and gain computational efficiency in the variable selection process. To analyse the performance, the presented methodologies are applied in simulated and real data. |
publishDate |
2022 |
dc.date.accessioned.fl_str_mv |
2022-02-23T18:24:34Z |
dc.date.available.fl_str_mv |
2022-02-23T18:24:34Z |
dc.date.issued.fl_str_mv |
2022-02-15 |
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 |
BOGONI, Mariella Ananias. Bayesian variable selection for logistic mixture models with Pólya-Gamma data augmentation. 2022. Dissertação (Mestrado em Estatística) – Universidade Federal de São Carlos, São Carlos, 2022. Disponível em: https://repositorio.ufscar.br/handle/ufscar/15643. |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufscar.br/handle/ufscar/15643 |
identifier_str_mv |
BOGONI, Mariella Ananias. Bayesian variable selection for logistic mixture models with Pólya-Gamma data augmentation. 2022. Dissertação (Mestrado em Estatística) – Universidade Federal de São Carlos, São Carlos, 2022. Disponível em: https://repositorio.ufscar.br/handle/ufscar/15643. |
url |
https://repositorio.ufscar.br/handle/ufscar/15643 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.confidence.fl_str_mv |
600 600 |
dc.relation.authority.fl_str_mv |
b32a2fc3-5d19-41db-9bab-08a95238ddf5 |
dc.rights.driver.fl_str_mv |
Attribution-NonCommercial-NoDerivs 3.0 Brazil http://creativecommons.org/licenses/by-nc-nd/3.0/br/ info:eu-repo/semantics/openAccess |
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Attribution-NonCommercial-NoDerivs 3.0 Brazil http://creativecommons.org/licenses/by-nc-nd/3.0/br/ |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Universidade Federal de São Carlos Câmpus São Carlos |
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Programa Interinstitucional de Pós-Graduação em Estatística - PIPGEs |
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UFSCar |
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Universidade Federal de São Carlos Câmpus São Carlos |
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