Thesis (M.S.) -- Worcester Polytechnic Institute. / Keywords: Gibbs Sampler; Bayesian Statistical Analysis; Ohlson Model; GIC Includes bibliographical references (p.79-80).

Thesis (Ph. D.)--Florida State University, 2006. / Advisor: Amy Chan Hilton, Florida State University, College of Engineering, Dept. of Civil and Environmental Engineering. Title and description from dissertation home page (viewed Sept. 18, 2006). Document formatted into pages; contains xiii, 107 pages. Includes bibliographical references.

Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

Thesis (Ph.D.)--Baylor University, 2006. / Includes bibliographical references (p. 77-81).

Thesis (Ph.D.)--Baylor University, 2006. / Includes bibliographical references (p. 115-117).

In many scientific and engineering researches, Bayesian surrogate models are utilized to handle nonlinear data for regression and classification tasks. In this thesis, we consider a real-life problem, functional response modeling of metamaterial and its rapid design, to which we establish and test such models. To familiarize with this subject, some fundamental electromagnetic physics are provided.. Noticing that the dispersive data are usually in rational form, a two-stage modeling approach is proposed, where in the first stage, a universal link function is formulated to rationally approximate the data with a few discrete parameters, namely poles and residues. Then they are used to synthesize equivalent circuits, and surrogate models are applied to circuit elements in the second stage.. To start with a regression scheme, the classical Gaussian process (GP) is introduced, which proceeds by parameterizing a covariance function of any continuous inputs, and infers hyperparameters given the training data. Two metamaterial prototypes are illustrated to demonstrate the methodology of model building, whose results are shown to prove the efficiency and precision of probabilistic pre- dictions. One well-known problem with metamaterial functionality is its great variability in resonance identities, which shows discrepancy in approximation orders required to fit the data with rational functions. In order to give accurate prediction, both approximation order and the presenting circuit elements should be inferred, by classification and regression, respectively. An augmented Bayesian surrogate model, which integrates GP multiclass classification, Bayesian treed GP regression, is formulated to provide a systematic dealing to such unique physical phenomenon. Meanwhile, the nonstationarity and computational complexity are well scaled with such model.. Finally, as one of the most advantageous property of Bayesian perspective, probabilistic assessment to underlying uncertainties is also discussed and demonstrated with detailed formulation and examples.

The estimation of variance components serves as an integral part of the evaluation of variation, and is of interest and required in a variety of applications (Hugo, 2012). Estimation of the among-group variance components is often desired for quantifying the variability and effectively understanding these measurements (Van Der Rijst, 2006). The methodology for determining Bayesian tolerance intervals for the one – way random effects model has originally been proposed by Wolfinger (1998) using both informative and non-informative prior distributions (Hugo, 2012). Wolfinger (1998) also provided relationships with frequentist methodologies. From a Bayesian point of view, it is important to investigate and compare the effect on coverage probabilities if negative variance components are either replaced by zero, or completely disregarded from the simulation process. This research presents a simulation-based approach for determining Bayesian tolerance intervals in variance component models when negative variance components are either replaced by zero, or completely disregarded from the simulation process. This approach handles different kinds of tolerance intervals in a straightforward fashion. It makes use of a computer-generated sample (Monte Carlo process) from the joint posterior distribution of the mean and variance parameters to construct a sample from other relevant posterior distributions. This research makes use of only non-informative Jeffreys‟ prior distributions and uses three Bayesian simulation methods. Comparative results of different tolerance intervals obtained using a method where negative variance components are either replaced by zero or completely disregarded from the simulation process, is investigated and discussed in this research.

Ideally, pavement management is a process of sequential decisions on a network of pavement sections. The network is subjected to uncertainties arising from material variability, random traffic, and fluctuating environmental inputs. The pavement manager optimizes the whole system subject to resource constraints, and avoids sub optimization of sections. The optimization process accounts for the dynamics of the pavement system. In addition to objective data the manager seeks information from a number of experts, and considers selected social-political factors and also potential implementation difficulties. Nine advanced schemes that have been developed for various pavement administrations are compared to the ideal. Although the schemes employ methods capable of handling the pavement system's complexities in isolation, not one can account for all complexities simultaneously. Bayesian decision analysis with recent extensions is useful for attacking the problem at hand. The method prescribes that when a decision maker is faced with a choice in an uncertain situation, he should pick the alternative with the maximum expected utility. To illustrate the potential of Bayesian decision analysis for pavement management, the author develops a Markov decision model for the operation of one pavement section. Consequences in each stage are evaluated by multi-attribute utility. The states are built of multiple pavement variables, such as strength, texture, roughness, etc. Group opinion and network optimization are recommended for future research, and decision analysis suggested as a promising way to attack these more complex problems. This thesis emphasizes the utility part of decision analysis, while it modifies an existing approach to handle the probability part. A procedure is developed for Bayesian updating of Markov transition matrices where the prior distributions are of the beta class, and are based on surveys of pavement condition and on engineering judgement. Preferences of six engineers are elicited and tested in a simulated decision situation. Multi-attribute utility theory is a reasonable approximation of the elicited value judgements and provides an expedient analytical tool. The model is programmed in PL1 and an example problem is analysed by a computer. Conclusions discuss the pavement maintenance problem from the decision analytical perspective. A revision is recommended of the widespread additive evaluation models from the standpoint of principles for rational choice. Those areas of decision theory which may be of interest to the pavement engineer, and to the civil engineer in general, are suggested for further study and monitoring. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

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