Use este identificador para citar ou linkar para este item: http://repositorio.ufla.br/jspui/handle/1/49599
Título: Processo de Cox marcado modulado por processos Gaussianos para configurações pontuais unidimensionais
Título(s) alternativo(s): Gaussian processes modulated marked Cox process for one-dimensional point patterns
Autores: Scalon, João Domingos
Oliveira, Deive Ciro de
Freire, Evelise Roman Corbalan Gois
Bueno Filho, Julio Silvio de Sousa
Oliveira, Marcelo Silva de
Nogueira, Denismar Alves
Palavras-chave: Inferência Bayesiana variacional
Modelagem em processos pontuais
Processos Gaussianos esparsos multivariados
Variational Bayesian inference
Point process modeling
Multivariate sparse Gaussian process
Data do documento: 28-Mar-2022
Editor: Universidade Federal de Lavras
Citação: FERREIRA, R. A. Processo de Cox marcado modulado por processos Gaussianos para configurações pontuais unidimensionais. 2022. 142 p. Tese (Doutorado em Estatística e Experimentação Agropecuária) – Universidade Federal de Lavras, Lavras, 2022.
Resumo: The theory of point processes is a very important Statistics area to describe the behavior of a certain random phenomenon whose realization results in a set of random points that represent occurrences of a point nature. These points, when indexed by the onedimensional set, they can represent the exact moment of occurrence. However, it can be defined in any indexing set, whether it is time or not. One of the ways to study a point process is through the intensity function, which describes an average rate of occurrences. It have been proposed several models to describe the behavior of the intensity of a point process in the literature, including the recent contribution of Lloyd et al. (2015), based on the Cox processes’ class in which the intensity function is described as a function of a stochastic Gaussian process . Lloyd et al. (2015) approach is based on a variational estimation method with the inclusion of a sparse method, which allows the model to handle a large number of observations. In addition, additional information associated with the occurrences of the point process can be incorporated into the model, which is called by marks. Thus, this thesis aimed to propose a modeling scheme to describe the intensity of a marked point processes, in which the mark is a qualitative variable, with two categories. The proposal was an extension of the Lloyd et al. (2015) model, in which the marked intensity function, based on two categories, was modeled as a function of a sparse bivariate Gaussian process. Following Lloyd et al. (2015), the estimation process was based on the Bayesian variational method, which allowed that the intensity function could be estimated for any point in the index set. As a way of exemplifying the proposal of this thesis, it was made an application from a set of real data based on the occurrence of accidents on Brazilian federal highways. The proposed model proved to be promising, suggesting that other extensions can be made so that the model can describe a much larger set of stochastic phenomena of a point nature.
URI: http://repositorio.ufla.br/jspui/handle/1/49599
Aparece nas coleções:Estatística e Experimentação Agropecuária - Doutorado (Teses)

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