Full Bayesian Significance Test para dados de sobrevivência bivariados: seleção de modelos encaixados da cópula PVF

• Ano de defesa: 2021
• Autor(a) principal: Cantoni, Murilo
• Orientador(a): Campos, Adriano Polpo de
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• 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: Análise de sobrevivência bivariada; Cópulas Arquimedianas; Dependência; Seleção de modelos
• Palavras-chave em Inglês: Full Bayesian Significance Test; Bivariate survival analysis; Archimedean copulas; Dependence; Model selection
• Área do conhecimento CNPq: CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::ANALISE DE DADOS
• Link de acesso: https://repositorio.ufscar.br/handle/20.500.14289/14810

The investigation and modeling of the existing dependence in a set of random variables is a widely discussed topic in statistics. In this context, the use of copulas becomes interesting because it is a flexible approach that allows to study, in a first moment, the univariate distributions and, later, the dependency structure. In practical problems, knowing the copula that best connects marginal distributions to the joint distribution function is not a simple task. In general, several models are adjusted according to the type of dependence existing in the data set and some selection criteria are applied in order to choose the "best model". In this work, we use the two-parameter Archimedean family of Power Variance Function (PVF), which includes the Clayton, Gumbel and Inverse Gaussian (IG) copulas as special or limiting cases, once it offers a unified and flexible approach to adjust widely used copula models and we propose the use of the Full Bayesian Significance Test (FBST) as a model selection criterion. We validated the results through a simulation study and illustrated the usefulness of the methodology using data on appendectomy times for adult twins.