Thesis--University of Wisconsin--Madison. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 64-66).

Thesis (Ph. D.)--University of Wisconsin--Madison, 1982. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 156-159).

Thesis (M.S.)--University of Missouri-Columbia, 2005. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (July 13, 2006) Includes bibliographical references.

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.)--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.

The Bayesian theory has long been the predominate method in dealing with uncertainties in civil engineering practice including water resources engineering. However, it imposes unnecessary restrictive requirements on inferential problems. Concerns thus arise about the effectiveness of using Bayesian theory in dealing with more general inferential problems. The recently developed Dempster-Shafer theory appears to be able to surmount the limitations of Bayesian theory. The new theory was originally proposed as a pure mathematical theory. A reasonable amount of work has been done in trying to adopt this new theory in practice, most of this work being related to inexact inference in expert systems and all of the work still remaining in the fundamental stage. The purpose of this research is first to compare the two theories and second to try to apply Dempster-Shafer theory in solving real problems in water resources engineering. In comparing Bayesian and Dempster-Shafer theory, the equivalent situation between these two theories under a special situation is discussed first. The divergence of results from Dempster-Shafer and Bayesian approaches under more general situations where Bayesian theory is unsatisfactory is then examined. Following this, the conceptual difference between the two theories is argued. Also discussed in the first part of this research is the issue of dealing with evidence including classifying sources of evidence and expressing them through belief functions. In attempting to adopt Dempster-Shafer theory in engineering practice, the Dempster-Shafer decision theory, i.e. the application of Dempster-Shafer theory within the framework of conventional decision theory, is introduced. The application of this new decision theory is demonstrated through a water resources engineering design example. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate