A comparação e seleção de modelos estatísticos desempenham um papel fundamental dentro da análise econométrica. No que se trata especificamente da avaliação de modelos não aninhados, o procedimento de teste denominado de J-Teste aparece como uma ferramenta de uso freqüente nessa literatura. De acordo com apontamentos, entre os anos de 1984 e 2004 o J-Teste foi citado em 497 artigos pertinentes. Diferentemente do J-Teste, as abordagens Bayesianas possuem um potencial de aplicabilidade ainda pouco explorado na literatura, dado que são metodologicamente coerentes com os procedimentos inferenciais da econometria. Nesse sentido, o objetivo do presente trabalho é o de avaliar a aplicabilidade do procedimento de teste Bayesiano FBST para a comparação de modelos econométricos não aninhados. Implementando-se o FBST para os mesmos dados de estudos estatísticos relevantes na Teoria Econômica, tais como Bremmer (2003) (Curva de Phillips) e Caporale e Grier (2000) (determinação da taxa de juros real), constata-se que os resultados obtidos apontam para conclusões semelhantes daquelas delineadas com a utilização do J-Teste. Além disso, ao se utilizar a noção de função poder para avaliar ambos os procedimentos de teste, observa-se que sob certas condições as chances de erro expressas pelo Erro Tipo I e Erro Tipo II se tornam relativamente próximas. / The comparison and selection of statistical models play an important role in econometric analysis. Dealing with evaluation of non nested models, the test procedure called J-Test is a frequently used tool in the literature. Accordingly to statistics, between the years 1894 and 2004 the J-Test was cited on 497 pertinent articles. Differently from J-Test, the Bayesian theories have an unexplored applicability potential in the literature, once they are methodologically coherent with the standard procedures of inference in econometrics. In this sense, the objective of this essay is to evaluate the applicability of the Bayesian procedure FBST to comparison of non nested econometric models. Implementing the FBST to the same data of some relevant statistical studies in Economic Theory, like Bremmer (2003) (Phillips Curve) and Caporale and Grier (2000) (real interest rate determination), it can be seen that the results obtained point to the same conclusions as that attained with J-Test utilization. Besides that, when implementing the power function to evaluate both test procedures, it can be observed that under some conditions the error chances expressed by Error Type I and Error Type II become relatively close.

A comparação e seleção de modelos estatísticos desempenham um papel fundamental dentro da análise econométrica. No que se trata especificamente da avaliação de modelos não aninhados, o procedimento de teste denominado de J-Teste aparece como uma ferramenta de uso freqüente nessa literatura. De acordo com apontamentos, entre os anos de 1984 e 2004 o J-Teste foi citado em 497 artigos pertinentes. Diferentemente do J-Teste, as abordagens Bayesianas possuem um potencial de aplicabilidade ainda pouco explorado na literatura, dado que são metodologicamente coerentes com os procedimentos inferenciais da econometria. Nesse sentido, o objetivo do presente trabalho é o de avaliar a aplicabilidade do procedimento de teste Bayesiano FBST para a comparação de modelos econométricos não aninhados. Implementando-se o FBST para os mesmos dados de estudos estatísticos relevantes na Teoria Econômica, tais como Bremmer (2003) (Curva de Phillips) e Caporale e Grier (2000) (determinação da taxa de juros real), constata-se que os resultados obtidos apontam para conclusões semelhantes daquelas delineadas com a utilização do J-Teste. Além disso, ao se utilizar a noção de função poder para avaliar ambos os procedimentos de teste, observa-se que sob certas condições as chances de erro expressas pelo Erro Tipo I e Erro Tipo II se tornam relativamente próximas. / The comparison and selection of statistical models play an important role in econometric analysis. Dealing with evaluation of non nested models, the test procedure called J-Test is a frequently used tool in the literature. Accordingly to statistics, between the years 1894 and 2004 the J-Test was cited on 497 pertinent articles. Differently from J-Test, the Bayesian theories have an unexplored applicability potential in the literature, once they are methodologically coherent with the standard procedures of inference in econometrics. In this sense, the objective of this essay is to evaluate the applicability of the Bayesian procedure FBST to comparison of non nested econometric models. Implementing the FBST to the same data of some relevant statistical studies in Economic Theory, like Bremmer (2003) (Phillips Curve) and Caporale and Grier (2000) (real interest rate determination), it can be seen that the results obtained point to the same conclusions as that attained with J-Test utilization. Besides that, when implementing the power function to evaluate both test procedures, it can be observed that under some conditions the error chances expressed by Error Type I and Error Type II become relatively close.

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Image segmentation is a critical step in building a computer vision algorithm that is able to distinguish between separate objects in an image scene. Image segmentation is based on two fundamentally intertwined components: pixel comparison and pixel grouping. In the pixel comparison step, pixels are determined to be similar or different from each other. In pixel grouping, those pixels which are similar are grouped together to form meaningful regions which can later be processed. This thesis makes original contributions to both of those areas. First, given a Markov Random Field framework, a Stochastic Nested Aggregation (SNA) framework for pixel and region grouping is presented and thoroughly analyzed using a Potts model. This framework is applicable in general to graph partitioning and discrete estimation problems where pairwise energy models are used. Nested aggregation reduces the computational complexity of stochastic algorithms such as Simulated Annealing to order O(N) while at the same time allowing local deterministic approaches such as Iterated Conditional Modes to escape most local minima in order to become a global deterministic optimization method. SNA is further enhanced by the introduction of a Graduated Models strategy which allows an optimization algorithm to converge to the model via several intermediary models. A well-known special case of Graduated Models is the Highest Confidence First algorithm which merges pixels or regions that give the highest global energy decrease. Finally, SNA allows us to use different models at different levels of coarseness. For coarser levels, a mean-based Potts model is introduced in order to compute region-to-region gradients based on the region mean and not edge gradients. Second, we develop a probabilistic framework based on hypothesis testing in order to achieve color constancy in image segmentation. We develop three new shading invariant semi-metrics based on the Dichromatic Reflection Model. An RGB image is transformed into an R'G'B' highlight invariant space to remove any highlight components, and only the component representing color hue is preserved to remove shading effects. This transformation is applied successfully to one of the proposed distance measures. The probabilistic semi-metrics show similar performance to vector angle on images without saturated highlight pixels; however, for saturated regions, as well as very low intensity pixels, the probabilistic distance measures outperform vector angle. Third, for interferometric Synthetic Aperture Radar image processing we apply the Potts model using SNA to the phase unwrapping problem. We devise a new distance measure for identifying phase discontinuities based on the minimum coherence of two adjacent pixels and their phase difference. As a comparison we use the probabilistic cost function of Carballo as a distance measure for our experiments.

Image segmentation is a critical step in building a computer vision algorithm that is able to distinguish between separate objects in an image scene. Image segmentation is based on two fundamentally intertwined components: pixel comparison and pixel grouping. In the pixel comparison step, pixels are determined to be similar or different from each other. In pixel grouping, those pixels which are similar are grouped together to form meaningful regions which can later be processed. This thesis makes original contributions to both of those areas. First, given a Markov Random Field framework, a Stochastic Nested Aggregation (SNA) framework for pixel and region grouping is presented and thoroughly analyzed using a Potts model. This framework is applicable in general to graph partitioning and discrete estimation problems where pairwise energy models are used. Nested aggregation reduces the computational complexity of stochastic algorithms such as Simulated Annealing to order O(N) while at the same time allowing local deterministic approaches such as Iterated Conditional Modes to escape most local minima in order to become a global deterministic optimization method. SNA is further enhanced by the introduction of a Graduated Models strategy which allows an optimization algorithm to converge to the model via several intermediary models. A well-known special case of Graduated Models is the Highest Confidence First algorithm which merges pixels or regions that give the highest global energy decrease. Finally, SNA allows us to use different models at different levels of coarseness. For coarser levels, a mean-based Potts model is introduced in order to compute region-to-region gradients based on the region mean and not edge gradients. Second, we develop a probabilistic framework based on hypothesis testing in order to achieve color constancy in image segmentation. We develop three new shading invariant semi-metrics based on the Dichromatic Reflection Model. An RGB image is transformed into an R'G'B' highlight invariant space to remove any highlight components, and only the component representing color hue is preserved to remove shading effects. This transformation is applied successfully to one of the proposed distance measures. The probabilistic semi-metrics show similar performance to vector angle on images without saturated highlight pixels; however, for saturated regions, as well as very low intensity pixels, the probabilistic distance measures outperform vector angle. Third, for interferometric Synthetic Aperture Radar image processing we apply the Potts model using SNA to the phase unwrapping problem. We devise a new distance measure for identifying phase discontinuities based on the minimum coherence of two adjacent pixels and their phase difference. As a comparison we use the probabilistic cost function of Carballo as a distance measure for our experiments.