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

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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