A inferência Bayesiana está cada vez mais dependente de algoritmos de simulação estocástica, e sua eficiência está diretamente relacionada à eficiência do algoritmo considerado. Uma prática bastante utilizada é a introdução de variáveis auxiliares para obtenção de formas conhecidas para as distribuições {\\it a posteriori} condicionais completas, as quais facilitam a implementação do amostrador de Gibbs. No entanto, a introdução dessas variáveis pode produzir algoritmos onde os valores simulados são fortemente correlacionados, fato esse que prejudica a convergência. O agrupamento das quantidades desconhecidas em blocos, de tal maneira que seja viável a simulação conjunta destas quantidades, é uma alternativa para redução da autocorrelação, e portanto, ajuda a melhorar a eficiência do procedimento de simulação. Neste trabalho, apresentamos propostas de simulação em blocos no contexto de modelos de regressão binária com o uso de variáveis auxiliares. Três classes de funções de ligação são consideradas: probito, logito e probito-assimétrico. Para as duas primeiras apresentamos e implementamos as propostas de atualização conjunta feitas por Holmes e Held (2006). Para a ligação probito-assimétrico propomos quatro diferentes maneiras de construir os blocos, e comparamos estes algoritmos através de duas medidas de eficiência (distância média Euclidiana entre atualizações e tamanho efetivo da amostra). Concluímos que os algoritmos propostos são mais eficientes que o convencional (sem blocos), sendo que um deles proporcionou ganho superior a 160\\% no tamanho efetivo da amostra. Além disso, discutimos uma etapa bastante importante da modelagem, denominada análise de resíduos. Nesta parte adaptamos e implementamos os resíduos propostos para a ligação probito para os modelos logístico e probito-assimétrico. Finalmente, utilizamos os resíduos propostos para verificar a presença de observações discrepantes em um conjunto de dados simulados. / The Bayesian inference is getting more and more dependent of stochastic simulation algorithms, and its efficiency is directly related with the efficiency of the considered algorithm. The introduction of auxiliary variables is a technique widely used for attainment of the full conditional distributions, which facilitate the implementation of the Gibbs sampling. However, the introduction of these auxiliary variables can produce algorithms with simulated values highly correlated, this fact harms the convergence. The grouping of the unknow quantities in blocks, in such way that the joint simulation of this quantities is possible, is an alternative for reduction of the autocorrelation, and therefore, improves the efficiency of the simulation procedure. In this work, we present proposals of simulation using the Gibbs block sampler in the context of binary response regression models using auxiliary variables. Three class of links are considered: probit, logit and skew-probit. For the two first we present and implement the scheme of joint update proposed by Holmes and Held (2006). For the skew-probit, we consider four different ways to construct the blocks, and compare these algorithms through two measures of efficiency (the average Euclidean update distance between interactions and effective sample size). We conclude that the considered algorithms are more efficient than the conventional (without blocks), where one of these leading to around 160\\% improvement in the effective sample size. Moreover, we discuss one important stage of the modelling, called residual analysis. In this part we adapt and implement residuals considered in the probit model for the logistic and skew-probit models. For a simulated data set we detect the presence of outlier used the residuals proposed here for the different models.

A inferência Bayesiana está cada vez mais dependente de algoritmos de simulação estocástica, e sua eficiência está diretamente relacionada à eficiência do algoritmo considerado. Uma prática bastante utilizada é a introdução de variáveis auxiliares para obtenção de formas conhecidas para as distribuições {\\it a posteriori} condicionais completas, as quais facilitam a implementação do amostrador de Gibbs. No entanto, a introdução dessas variáveis pode produzir algoritmos onde os valores simulados são fortemente correlacionados, fato esse que prejudica a convergência. O agrupamento das quantidades desconhecidas em blocos, de tal maneira que seja viável a simulação conjunta destas quantidades, é uma alternativa para redução da autocorrelação, e portanto, ajuda a melhorar a eficiência do procedimento de simulação. Neste trabalho, apresentamos propostas de simulação em blocos no contexto de modelos de regressão binária com o uso de variáveis auxiliares. Três classes de funções de ligação são consideradas: probito, logito e probito-assimétrico. Para as duas primeiras apresentamos e implementamos as propostas de atualização conjunta feitas por Holmes e Held (2006). Para a ligação probito-assimétrico propomos quatro diferentes maneiras de construir os blocos, e comparamos estes algoritmos através de duas medidas de eficiência (distância média Euclidiana entre atualizações e tamanho efetivo da amostra). Concluímos que os algoritmos propostos são mais eficientes que o convencional (sem blocos), sendo que um deles proporcionou ganho superior a 160\\% no tamanho efetivo da amostra. Além disso, discutimos uma etapa bastante importante da modelagem, denominada análise de resíduos. Nesta parte adaptamos e implementamos os resíduos propostos para a ligação probito para os modelos logístico e probito-assimétrico. Finalmente, utilizamos os resíduos propostos para verificar a presença de observações discrepantes em um conjunto de dados simulados. / The Bayesian inference is getting more and more dependent of stochastic simulation algorithms, and its efficiency is directly related with the efficiency of the considered algorithm. The introduction of auxiliary variables is a technique widely used for attainment of the full conditional distributions, which facilitate the implementation of the Gibbs sampling. However, the introduction of these auxiliary variables can produce algorithms with simulated values highly correlated, this fact harms the convergence. The grouping of the unknow quantities in blocks, in such way that the joint simulation of this quantities is possible, is an alternative for reduction of the autocorrelation, and therefore, improves the efficiency of the simulation procedure. In this work, we present proposals of simulation using the Gibbs block sampler in the context of binary response regression models using auxiliary variables. Three class of links are considered: probit, logit and skew-probit. For the two first we present and implement the scheme of joint update proposed by Holmes and Held (2006). For the skew-probit, we consider four different ways to construct the blocks, and compare these algorithms through two measures of efficiency (the average Euclidean update distance between interactions and effective sample size). We conclude that the considered algorithms are more efficient than the conventional (without blocks), where one of these leading to around 160\\% improvement in the effective sample size. Moreover, we discuss one important stage of the modelling, called residual analysis. In this part we adapt and implement residuals considered in the probit model for the logistic and skew-probit models. For a simulated data set we detect the presence of outlier used the residuals proposed here for the different models.

This thesis discusses two aspects of spatial statistics: sampling and prediction. In spatial statistics, we observe some phenomena in space. Space is typically of two or three dimensions, but can be of higher dimension. Questions in mind could be; What is the total amount of gold in a gold-mine? How much precipitation could we expect in a specific unobserved location? What is the total tree volume in a forest area? In spatial sampling the aim is to estimate global quantities, such as population totals, based on samples of locations (papers III and IV). In spatial prediction the aim is to estimate local quantities, such as the value at a single unobserved location, with a measure of uncertainty (papers I, II and V). In papers III and IV, we propose sampling designs for selecting representative probability samples in presence of auxiliary variables. If the phenomena under study have clear trends in the auxiliary space, estimation of population quantities can be improved by using representative samples. Such samples also enable estimation of population quantities in subspaces and are especially needed for multi-purpose surveys, when several target variables are of interest. In papers I and II, the objective is to construct valid prediction intervals for the value at a new location, given observed data. Prediction intervals typically rely on the kriging predictor having a Gaussian distribution. In paper I, we show that the distribution of the kriging predictor can be far from Gaussian, even asymptotically. This motivated us to propose a semiparametric method that does not require distributional assumptions. Prediction intervals are constructed from the plug-in ordinary kriging predictor. In paper V, we consider prediction in the presence of left-censoring, where observations falling below a minimum detection limit are not fully recorded. We review existing methods and propose a semi-naive method. The semi-naive method is compared to one model-based method and two naive methods, all based on variants of the kriging predictor.

The aim of this thesis is to describe and further develop estimation strategies for data obtained by stratified sampling. Estimation of the mean and linear regression model are discussed. The possible inclusion of auxiliary variables in the estimation is exam- ined. The auxiliary variables can be transformed rather than used in their original form. A transformation minimizing the asymptotic variance of the resulting estimator is pro- vided. The estimator using an approach from this thesis is compared to the doubly robust estimator and shown to be asymptotically equivalent.

In this thesis, we discuss calibration estimation in the presence of nonresponse with a focus on the linear calibration estimator and the propensity calibration estimator, along with the use of different levels of auxiliary information, that is, sample and population levels. This is a fourpapers- based thesis, two of which discuss estimation in two steps. The two-step-type estimator here suggested is an improved compromise of both the linear calibration and the propensity calibration estimators mentioned above. Assuming that the functional form of the response model is known, it is estimated in the first step using calibration approach. In the second step the linear calibration estimator is constructed replacing the design weights by products of these with the inverse of the estimated response probabilities in the first step. The first step of estimation uses sample level of auxiliary information and we demonstrate that this results in more efficient estimated response probabilities than using population-level as earlier suggested. The variance expression for the two-step estimator is derived and an estimator of this is suggested. Two other papers address the use of auxiliary variables in estimation. One of which introduces the use of principal components theory in the calibration for nonresponse adjustment and suggests a selection of components using a theory of canonical correlation. Principal components are used as a mean to accounting the problem of estimation in presence of large sets of candidate auxiliary variables. In addition to the use of auxiliary variables, the last paper also discusses the use of explicit models representing the true response behavior. Usually simple models such as logistic, probit, linear or log-linear are used for this purpose. However, given a possible complexity on the structure of the true response probability, it may raise a question whether these simple models are effective. We use an example of telephone-based survey data collection process and demonstrate that the logistic model is generally not appropriate.