Modelos aproximados e exatos para geoestatística com amostragem preferencial

• Ano de defesa: 2021
• Autor(a) principal: Douglas Mateus da Silva
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Minas Gerais; Brasil; ICX - DEPARTAMENTO DE ESTATÍSTICA; Programa de Pós-Graduação em Estatística; UFMG
• Palavras-chave em Português: Geoestatística; Amostragem preferencial; Inferência clássica; Inferência Bayesiana; Outlier; t-Student; Geostatistics; Preferential sampling; Classic inference; Bayesian inference; Estatística – Teses; Geologia – Métodos estatísticos – Tese; Amostragem (Estatística) – Teses; Teoria bayesiana de decisão estatística – Teses
• Link de acesso: http://hdl.handle.net/1843/39050

Geostatistical models are used to analyze spatially correlated data under a continuous domain. The traditional methodology of geostatistics supposes that the sampling design is constructed independently of the phenomena in the study and we denominate this sampling process as non preferential. When the sampling design is constructed with information about the variable of interest, some locals have more chance of being selected in comparison to others. This kind of sampling we denominate preferential. Under the preferential sampling, the latent process that models data and the pontual process that models the spacial configuration of the sample are not independent. We can not ignore the join distribution of those processes, because we will obtain biased results under estimation and prediction. Since the EM algorithm is a method that deals with latent data, it is natural to consider it as a tool of estimation for this model. In this way, the first aim in this thesis is the development of an SAEM algorithm for parameter estimation of the model under preferential sampling, in the classic approach. Besides this, in presence of outliers, the Gaussian model is not adequate and we have to consider heavier tails distributions. We developed a geostatistical model under preferential sampling with t-Student distribution to deal with this problem, beign this the second aim of this thesis. In the existent literature, it assumes the exponential function as the intensity function of the pontual process, which has intractable likelihood function. In this case, the inference is realized considering discrete approximation of the region in study, which can lead to errors that are difficult to measure. In this way, as the third aim of this thesis, we developed an exact Bayesian model for geostatistical data under preferential sampling. Simulated examples are considered to evaluate the methodology proposed for the three aims of this thesis, as well application on real data, one of them being the moss data of Galicia, a dataset well known in the literature. The proposed models provided better results in parameter estimation and prediction of the variable of interest on locals that were not sampled compared to the existing methods, mainly in regions that are distant of locals sampled which the quantity of information is low.