No description available.

This thesis develops techniques for adjusting for selection bias using Gaussian process models. Selection bias is a key issue both in sample surveys and in observational studies for causal inference. Despite recently emerged techniques for dealing with selection bias in high-dimensional or complex situations, use of Gaussian process models and Bayesian hierarchical models in general has not been explored. Three approaches are developed for using Gaussian process models to estimate the population mean of a response variable with binary selection mechanism. The first approach models only the response with the selection probability being ignored. The second approach incorporates the selection probability when modeling the response using dependent Gaussian process priors. The third approach uses the selection probability as an additional covariate when modeling the response. The third approach requires knowledge of the selection probability, while the second approach can be used even when the selection probability is not available. In addition to these Gaussian process approaches, a new version of the Horvitz-Thompson estimator is also developed, which follows the conditionality principle and relates to importance sampling for Monte Carlo simulations. Simulation studies and the analysis of an example due to Kang and Schafer show that the Gaussian process approaches that consider the selection probability are able to not only correct selection bias effectively, but also control the sampling errors well, and therefore can often provide more efficient estimates than the methods tested that are not based on Gaussian process models, in both simple and complex situations. Even the Gaussian process approach that ignores the selection probability often, though not always, performs well when some selection bias is present. These results demonstrate the strength of Gaussian process models in dealing with selection bias, especially in high-dimensional or complex situations. These results also demonstrate that Gaussian process models can be implemented rather effectively so that the benefits of using Gaussian process models can be realized in practice, contrary to the common belief that highly flexible models are too complex to use practically for dealing with selection bias.

Geometric quality variables of wafers, such as BOW and WARP, are critical in their applications. A large variation of these quality variables reduces the number of conforming products in the downstream production. Therefore, it is important to reduce the variation by variation modeling, analysis and control for multistage wafer manufacturing processes (MWMPs). First, an intermediate feedforward control strategy is developed to adjust and update the control actions based on the online measurements of intermediate wafer quality measurements. The control performance is evaluated in a MWMP to transform ingots into polished wafers. However, in a complex multistage manufacturing process, the quality variables may have nonlinear relationship with the parameters of the predictors. In this case, piecewise linear regression tree (PLRT) models are used to address nonlinear relationships in MWMP to improve the model prediction performance. The obtained PLRT model is further reconfigured to be complied with the physical layout of the MWMP for feedforward control purposes. The procedure and effectiveness of the proposed method is shown in a case study of a MWMP. Furthermore, as the geometric profiles and quality variables are important quality features for a wafer, fast and accurate measurements of those features are crucial for variation reduction and feedforward control. A sequential measurement strategy is proposed to reduce the number of samples measured in a wafer, yet provide adequate accuracy for the quality feature estimation. A Gaussian process model is used to estimate the true profile of a wafer with improved sensing efficiency. Finally, we study the multistage multimode process monitoring problem. We propose to use PLRTs to inter-relate the variables in a multistage multimode process. A unified charting system is developed. We further study the run length distribution, and optimize the control chart system by considering the modeling uncertainties. Finally, we compare the proposed method with the risk adjustment type of control chart systems based on global regression models, for both simulation study and a wafer manufacturing process.

The use of computer modeling is fast increasing in almost every scientific, engineering and business arena. This dissertation investigates some challenging issues in design, modeling and analysis of computer experiments, which will consist of four major parts. In the first part, a new approach is developed to combine data from approximate and detailed simulations to build a surrogate model based on some stochastic models. In the second part, we propose some Bayesian hierarchical Gaussian process models to integrate data from different types of experiments. The third part concerns the development of latent variable models for computer experiments with multivariate response with application to data center temperature modeling. The last chapter is devoted to the development of nested space-filling designs for multiple experiments with different levels of accuracy.

Cette thèse traite de stratégies d'évaluation séquentielle et batch-séquentielle de fonctions à valeurs réelles sous un budget d'évaluation limité, à l'aide de modèles à processus Gaussiens. Des stratégies optimales de réduction séquentielle d'incertitude (SUR) sont étudiées pour deux problèmes différents, motivés par des cas d'application en sûreté nucléaire. Tout d'abord, nous traitons le problème d'identification d'un ensemble d'excursion au dessus d'un seuil T d'une fonction f à valeurs réelles. Ensuite, nous étudions le problème d'identification de l'ensemble des configurations "robustes, contrôlées", c'est à dire l'ensemble des inputs contrôlés où la fonction demeure sous T quelle que soit la valeur des différents inputs non-contrôlés. De nouvelles stratégies SUR sont présentés. Nous donnons aussi des procédures efficientes et des formules permettant d'utiliser ces stratégies sur des applications concrètes. L'utilisation de formules rapides pour recalculer rapidement le posterior de la moyenne ou de la fonction de covariance d'un processus Gaussien (les "formules d'update de krigeage") ne fournit pas uniquement une économie computationnelle importante. Elles sont aussi l'un des ingrédient clé pour obtenir des formules fermées permettant l'utilisation en pratique de stratégies d'évaluation coûteuses en temps de calcul. Une contribution en optimisation batch-séquentielle utilisant le Multi-points Expected Improvement est également présentée.