This thesis deals with the development and application of numerical integration techniques for use in Bayesian Statistics. In particular, it describes how imbedded sequences of positive interpolatory integration rules (PIIR's) obtained from Gauss-Hermite product rules can extend the applicability and efficiency of currently available numerical methods. The numerical strategy suggested by Naylor and Smith (1982) is reviewed, criticised and applied to some examples with real and artificial data. The performance of this strategy is assessed from the viewpoint of 3 criteria: reliability, efficiency and accuracy. The imbedded sequences of PIIR’s are introduced as an alternative and an extension to the above strategy for two major reasons. Firstly, they provide a rich class of spatially ditributed rules which are particularly useful in high dimensions. Secondly, they provide a way of producing more efficient integration strategies by enabling approximations to be updated sequentially through the addition of new nodes at each step rather than through changing to a completely new set of nodes. Finally, the Improvement in the reliability and efficiency achieved by the adaption of an integration strategy based on PIIR's is demonstrated with various illustrative examples. Moreover, it is directly compared with the Gibbs sampling approach introduced recently by Gelfand and Smith (1988).

Neste trabalho é analisado o problema elástico tridimensional através do método dos elementos de contorno empregando a solução fundamental de Kelvin. São utilizadas duas formulações principais: a formulação clássica e a formulação hiper-singular. A primeira utiliza a solução fundamental de Kelvin clássica e a segunda aplica uma derivada direcional da solução fundamental de Kelvin. O contorno é discretizado utilizando-se elemento triangular plano com aproximações constante, linear e quadrática. As integrais singulares são desenvolvidas analiticamente para o elemento constante, e semi-analiticamente para os elementos linear e quadrático. São apresentadas técnicas de integração de contorno considerando-se a eficiência e a precisão para a integral quase singular. São apresentados vários exemplos numéricos, inclusive problemas esbeltos, e seus resultados são comparados com valores conhecidos pela teoria de elasticidade, ou ainda, comparados com valores disponíveis na literatura. / In this work the three-dimensional elastic problem is analyzed by the boundary element method using the Kelvin fundamental solution. Two main formulations are applied. The first one uses the classical Kelvin fundamental solution and the other, hyper-singular, uses a derivative of the Kelvin fundamental solution. The boundary is discretized by flat triangular elements with constant, linear and quadratic approximations. The singular integrals are analytically developed for constant elements, while for linear and quadratic elements a semi-analytical process is employed. Different techniques to perform quasi-singular boundary integrals are presented and their efficiency and accuracy are compared. Several numerical examples are presented, including slender problems. The results are compared with known solutions given by the theory of elasticity, or with other results found in the literature.

Neste trabalho é analisado o problema elástico tridimensional através do método dos elementos de contorno empregando a solução fundamental de Kelvin. São utilizadas duas formulações principais: a formulação clássica e a formulação hiper-singular. A primeira utiliza a solução fundamental de Kelvin clássica e a segunda aplica uma derivada direcional da solução fundamental de Kelvin. O contorno é discretizado utilizando-se elemento triangular plano com aproximações constante, linear e quadrática. As integrais singulares são desenvolvidas analiticamente para o elemento constante, e semi-analiticamente para os elementos linear e quadrático. São apresentadas técnicas de integração de contorno considerando-se a eficiência e a precisão para a integral quase singular. São apresentados vários exemplos numéricos, inclusive problemas esbeltos, e seus resultados são comparados com valores conhecidos pela teoria de elasticidade, ou ainda, comparados com valores disponíveis na literatura. / In this work the three-dimensional elastic problem is analyzed by the boundary element method using the Kelvin fundamental solution. Two main formulations are applied. The first one uses the classical Kelvin fundamental solution and the other, hyper-singular, uses a derivative of the Kelvin fundamental solution. The boundary is discretized by flat triangular elements with constant, linear and quadratic approximations. The singular integrals are analytically developed for constant elements, while for linear and quadratic elements a semi-analytical process is employed. Different techniques to perform quasi-singular boundary integrals are presented and their efficiency and accuracy are compared. Several numerical examples are presented, including slender problems. The results are compared with known solutions given by the theory of elasticity, or with other results found in the literature.

Data on the Web in HTML tables is mostly structured, but we usually do not know the structure in advance. Thus, we cannot directly query for data of interest. We propose a solution to this problem for the case of mostly structured data in the form of HTML tables, based on document-independent extraction ontologies. The solution entails elements of table location and table understanding, data integration, and wrapper creation. Table location and understanding allows us to locate the table of interest, recognize attributes and values, pair attributes with values, and form records. Data-integration techniques allow us to match source records with a target schema. Ontologically specified wrappers allow us to extract data from source records into a target schema. Experimental results show that we can successfully map data of interest from source HTML tables with unknown structure to a given target database schema. We can thus "directly" query source data with unknown structure through a known target schema.

In this thesis, we analyze the performance of the Post Detection Integration (PDI) techniques used for detection of weak DS/CDMA signals in the presence of uncertainty in the frequency, noise variance and data bits. Such weak signal detection problems arise, for example, in the first step of code acquisition for applications such as the Global Navigation Satellite Systems (GNSS) based position localization. Typically, in such applications, a combination of coherent and post-coherent integration stages are used to improve the reliability of signal detection. We show that the feasibility of using fully coherent processing is limited due to the presence of unknown data-bits and/or frequency uncertainty. We analyze the performance of the two conventional PDI techniques, namely, the Non-coherent PDI (NC-PDI) and the Differential-PDI (D-PDI), in the presence of noise and data bit uncertainty, to establish their robustness for weak signal detection. We show that the NC-PDI technique is robust to uncertainty in the data bits, but a fundamental detection limit exists due to uncertainty in the noise variance. The D-PDI technique, on the other hand, is robust to uncertainty in the noise variance, but its performance degrades in the presence of unknown data bits. We also analyze the following different variants of the NC-PDI and D-PDI techniques: Quadratic NC-PDI technique, Non-quadratic NC-PDI, D-PDI with real component (D-PDI (Real)) and D-PDI with absolute component (D-PDI (Abs)). We show that the likelihood ratio based test statistic derived in the presence of data bits is non-robust in the presence of noise uncertainty. We propose two novel PDI techniques as a solution to the above mentioned shortcomings in the conventional PDI methods. The first is a cyclostationarity based sub-optimal PDI technique, that exploits the periodicity introduced due to the data bits. We establish the exact mathematical relationship between the D-PDI and cyclostationarity-based signal detection methods. The second method we propose is a modified PDI technique, which is robust against both noise and data bit uncertainties. We derive two variants of the modified technique, which are tailored for data and pilot channels, respectively. We characterize the performance of the conventional and proposed PDI techniques in terms of their false alarm and detection probabilities and compare them through the receiver operating characteristic (ROC) curves. We derive the sample complexity of the test-statistic in order to achieve a given performance in terms of detection and false alarm probabilities in the presence of model uncertainties. We validate the theoretical results and illustrate the improved performance that can be obtained using our proposed PDI protocols through Monte-Carlo simulations.