Les métamodèles statistiques sont régulièrement confrontés au manque de données qui engendre des difficultés à estimer les paramètres. Le paradigme bayésien fournit un moyen élégant de contourner le problème en décrivant la connaissance que nous avons des paramètres par une loi de probabilité a posteriori au lieu de la résumer par une estimation ponctuelle. Cependant, ce paradigme nécessite de définir une loi a priori adéquate, ce qui est un exercice difficile en l'absence de jugement d'expert. L'école bayésienne objective propose des priors par défaut dans ce genre de situation telle que le prior de référence de Berger-Bernardo. Un tel prior a été calculé par Berger, De Oliveira and Sansó [2001] pour le modèle de krigeage avec noyau de covariance isotrope. Une extension directe au cas des noyaux anisotropes poserait des problèmes théoriques aussi bien que pratiques car la théorie de Berger-Bernardo ne peut s'appliquer qu'à un jeu de paramètres ordonnés. Or dans ce cas de figure, tout ordre serait nécessairement arbitraire. Nous y substituons une solution bayésienne objective fondée sur les posteriors de référence conditionnels. Cette solution est rendue possible par une théorie du compromis entre lois conditionnelles incompatibles. Nous montrons en outre qu'elle est compatible avec le krigeage trans-gaussien. Elle est appliquée à un cas industriel avec des données non-stationnaires afin de calculer des Probabilités de Détection de défauts (POD de l'anglais Probability Of Detection) par tests non-destructifs dans les tubes de générateur de vapeur de centrales nucléaires. / A recurring problem in surrogate modelling is the scarcity of available data which hinders efforts to estimate model parameters. The Bayesian paradigm offers an elegant way to circumvent the problem by describing knowledge of the parameters by a posterior probability distribution instead of a pointwise estimate. However, it involves defining a prior distribution on the parameter. In the absence of expert opinion, finding an adequate prior can be a trying exercise. The Objective Bayesian school proposes default priors for such can be a trying exercise. The Objective Bayesian school proposes default priors for such situations, like the Berger-Bernardo reference prior. Such a prior was derived by Berger, De Oliveira and Sansó [2001] for the Kriging surrogate model with isotropic covariance kernel. Directly extending it to anisotropic kernels poses theoretical as well as practical problems because the reference prior framework requires ordering the parameters. Any ordering would in this case be arbitrary. Instead, we propose an Objective Bayesian solution for Kriging models with anisotropic covariance kernels based on conditional reference posterior distributions. This solution is made possible by a theory of compromise between incompatible conditional distributions. The work is then shown to be compatible with Trans-Gaussian Kriging. It is applied to an industrial case with nonstationary data in order to derive Probability Of defect Detection (POD) by non-destructive tests in steam generator tubes of nuclear power plants.

In simple linear regression, it is assumed that two variables are linearly related, with unknown intercept and slope parameters. In particular, a regressor variable is assumed to be precisely measurable, and a response is assumed to be a random variable whose mean depends on the regressor via a linear function. For the simple linear regression problem, interest typically centers on estimation of the unknown model parameters, and perhaps application of the resulting estimated linear relationship to make predictions about future response values corresponding to given regressor values. The linear statistical calibration problem (or, more precisely, the absolute linear calibration problem), bears a resemblance to simple linear regression. It is still assumed that the two variables are linearly related, with unknown intercept and slope parameters. However, in calibration, interest centers on estimating an unknown value of the regressor, corresponding to an observed value of the response variable. We consider Bayesian methods of analysis for the linear statistical calibration problem, based on noninformative priors. Posterior analyses are assessed and compared with classical inference procedures. It is shown that noninformative prior Bayesian analysis is a strong competitor, yielding posterior inferences that can, in many cases, be correctly interpreted in a frequentist context. We also consider extensions of the linear statistical calibration problem to polynomial models and multivariate regression models. For these models, noninformative priors are developed, and posterior inferences are derived. The results are illustrated with analyses of published data sets. In addition, a certain type of heteroscedasticity is considered, which relaxes the traditional assumptions made in the analysis of a statistical calibration problem. It is shown that the resulting analysis can yield more reliable results than an analysis of the homoscedastic model. / Ph. D.

Published Article / An exploratory study was conducted to investigate firstly, the contextual problems first-year university students experienced at their respective schools and secondly, the subject related-problems that they could be bringing to science classes and which could later affect their understanding of science concepts. The study is grounded in constructivism. A questionnaire was administered to all the 2007 First-year B.Ed (FET) Natural Science students at the Central University of Technology, Free State. The contextual problems identified by respondents included school, educator, examiner and student-related problems. Subject specific problem areas were identified in biology, chemistry and physics. The paper also reports on the preliminary results of some teaching interventions implemented in the three subjects. A Force Concept Inventory (FCI) test was administered to the physics students, and a concept test for chemistry group. Concept mapping as a teaching and learning strategy has been introduced in biology classes. Further research continues on the effectiveness of these interventions.

Approved for public release; distribution is unlimited / This thesis describes a Bayesian method to determine the number of samples needed to estimate a proportion or probability with 95% confidence when prior bounds are placed on that proportion. It uses the Uniform [a,b] distribution as the prior, and develops a computer program and tables to find the sample size. Tables and examples are also given to compare these results with other approaches for finding sample size. The improvement that can be obtained with this method is fewer samples, and consequently less cost in Weapons Testing is required to meet a desired confidence size for a proportion or probability. / http://archive.org/details/bayesianmethodto00flor / Lieutenant Commander, Hellenic Navy

In social and economic studies many of the collected variables are measured on a nominal scale, often with a large number of categories. The definition of categories can be ambiguous and different classification schemes using either a finer or a coarser grid are possible. Categorization has an impact when such a variable is included as covariate in a regression model: a too fine grid will result in imprecise estimates of the corresponding effects, whereas with a too coarse grid important effects will be missed, resulting in biased effect estimates and poor predictive performance. To achieve an automatic grouping of the levels of a categorical covariate with essentially the same effect, we adopt a Bayesian approach and specify the prior on the level effects as a location mixture of spiky Normal components. Model-based clustering of the effects during MCMC sampling allows to simultaneously detect categories which have essentially the same effect size and identify variables with no effect at all. Fusion of level effects is induced by a prior on the mixture weights which encourages empty components. The properties of this approach are investigated in simulation studies. Finally, the method is applied to analyse effects of high-dimensional categorical predictors on income in Austria.

This work offers two strategies to raise the prediction accuracy of Vector Autoregressive (VAR) Models. The first strategy is to improve the Minnesota prior, which is frequently used for Bayesian VAR models. The improvement is achieved in two ways. First, the variance-covariance matrix of regression disturbances is treated as unknown and random to incorporate parameter uncertainty. Second, the prior variance-covariance matrix of regression coefficients is constructed as a function of the variance-covariance matrix of disturbances, in order to account for dependencies between different equations. Since different prior specifications unavoidably lead to different models, and forecasting capability of any such model is often limited, the second strategy is to build an optimal prediction pool of models by using the conventional log predictive score function. The effectiveness of the proposed strategies is examined for one-step-ahead, multi-4-step-ahead, and single-4-step-ahead predictions through two exercises. One exercise is predicting national output, inflation, and interest rate in the United States, and the other is predicting state tax revenue and personal income in Iowa. The empirical results indicate that a properly selected prior can improve the prediction performance of a BVAR model, and that a real-time optimal prediction pool can outperform a single best constituent model alone.

The general goal of this study was to investigate the feasibility of creating a constructivist learning environment in a university mathematics course as an alternative to the dominant transmissionist learning environments currently in place in most such courses. In order to accomplish this goal the researcher, a university professor, attempted to create this environment and document it in a case study.The study sought to ascertain which dimensions of a constructivist learning environment - autonomy, prior knowledge, negotiation, student-centeredness - university students preferred and how these preferences changed after being in such an environment. It also sought to find out how students' preferred environments matched the environment they perceived to be in place. In addition, the study sought to determine what changes the instructor had to make in his teaching practice to implement each of the dimensions.The results of the study suggest most students very strongly preferred the prior-knowledge and negotiation dimensions, strongly preferred the autonomy dimension, and weakly to moderately preferred the student-centeredness dimension. The data indicate that during the study student preferences for prior knowledge and negotiation increased slightly, preferences for student centeredness increased moderately, and preferences for autonomy increased significantly.In addition, the researcher found that the four dimensions were not implemented equally. While the first three dimensions were strongly implemented, the student-centeredness dimension was only moderately implemented. Interestingly, the learning environment the students perceived to be in place closely matched their preferences.

We had previously shown that regularization principles lead to approximation schemes, as Radial Basis Functions, which are equivalent to networks with one layer of hidden units, called Regularization Networks. In this paper we show that regularization networks encompass a much broader range of approximation schemes, including many of the popular general additive models, Breiman's hinge functions and some forms of Projection Pursuit Regression. In the probabilistic interpretation of regularization, the different classes of basis functions correspond to different classes of prior probabilities on the approximating function spaces, and therefore to different types of smoothness assumptions. In the final part of the paper, we also show a relation between activation functions of the Gaussian and sigmoidal type.

Information in a message can either be fully expressed (explicitly) or indirectly stated (implied) and understood by inference or association. Previous research suggested an age-related decline in performance of implicit compared to explicit information and that this relationship is moderated by prior knowledge. Whereas previous studies mainly obtained quantitative data of inferencing performance, the current study employed both quantitative and qualitative techniques to understand age-related differences in inferencing. Twenty younger and older participants evaluated whether a series of one-sentence statements were true or false based on specific two-sentence text passages. Text passages either resembled real warnings (taken from actual products) or were novel (the opposite of a warning found on an actual product). Statements either explicitly stated information from the text passage or required participants to go beyond information given in the text. Quantitative analysis showed that older adults accuracy compared to that of younger adults when evaluating real text passages, with explicit items being evaluated more accurately than implicit items. For novel text passages (generally lower accuracy scores), younger adults showed the same pattern as for real text passages, whereas older adults accuracy was low for both explicit and implicit statements. Qualitative analyses supported that participants correct answers generally reflected that the intended inference was drawn and that for incorrect answers the inference was not mentioned. The data also suggested that accuracy scores may underestimate the actual ability to infer. Both age groups mentioned most often that text-related factors (e.g., clarity) influenced their decision and brought outside information (e.g., education, experience, expectations) to the task regardless of text passage or statement type. Older adults more often referred to outside information than younger adults, particularly when evaluating novel text passages and their answer was wrong. This study substantiated that age-related differences in a task requiring inferencing may be explained by a combination of the factors of working memory (time and availability of information) and prior knowledge as well as a possible decline in inferencing ability. Prior knowledge is important for both age groups and especially so for older adults. Important implications for designers are to make information available and explicit.

This thesis explores, through fictional storytelling, the cultural duality of individuals inhabiting Singapore prior to World War II. The primary locale in many of these stories-an actual residence known as Eu Villa-interconnects each narrative and helps to uncover the hybridization of a Chinese family (and servants) living in a British colony. Many of the stories are imparted from different perspectives: wives, children and amahs, each of them pieced together to bridge the space between Chinese heritage overlaid and intermixed with British culture. In this way, the stories of this thesis reflect on the history that preceded the distinct multiculturalism of contemporary Singapore.