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Inference under uncertainty plays a crucial role in expert system and receives growing attention from artificial intelligence experts, statisticians, and psychologists. In searching for new satisfactory ways to model inference under uncertainty, it will be necessary to combine the efforts of researchers from different areas. It is expected that with deep insight into this crucial problem, it will not only have enormous impact on development of AI and expert system, but also bring classical areas like statistics into a new stage. This research paper gives a precise synopsis of present work in the field and explores the mechanics of statistical inference to a new depth by combining efforts of computer scientists, statisticians, and psychologists. One important part of the paper is the comparison of different paradigms, including the difference between statistical and logical views. Special attentions, which need to be paid when combining various methods, are considered in the paper. Also, some examples and counterexamples will be given to illustrate the availability of individual model which describes human behavior. Finally, a new framework to deal with uncertainty is proposed, and future trends of uncertainty management are projected. / Department of Mathematical Sciences

Thesis (Ph. D.)--University of Washington, 2007. / Vita. Includes bibliographical references (p. 124-130).

Thesis (M.S.M.E.)--University of Massachusetts Amherst, 2009. / Open access. "This protocol is the basis of an ongoing pilot study in conjunction with Cooley Dickinson Hospital, Northampton, MA."--P. vii. Includes bibliographical references (p. 118-121).

Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2002. / Includes bibliographical references (leaves 192-195). Also available in electronic version. Access restricted to campus users.

Ph.D. (Mathematics) / Please refer to full text to view abstract

The work described in this thesis stems from the idea that expert systems should be able to accurately and appropriately handle uncertain information. The traditional approaches to dealing with uncertainty are discussed and are shown to contain many inadequacies. The Dempster-Shafer, or D-S, theory of evidence is proposed as an appealing theoretical basis for representing uncertain knowledge and for performing inexact reasoning in expert systems. The D-S theory is reviewed in some detail; including its approaches to representing concepts, to representing belief, to combining belief and to performing inference. The D-S implementation approaches pursued by other researchers are described and critiqued. Attempts made early in the thesis research which failed to achieve the important goal of consistency with the D-S theory are also reviewed. Two approaches to implementing D-S theory in a completely consistent manner are discussed in detail. It is shown that the second of these systems, a frame network approach, has led to the development of a fully functional prototype expert system shell called FRO. In this system, concepts are represented using D-S frames of discernment, belief is represented using D-S belief functions, and inference is performed using stored relationships between frames of discernment (forming the frame network) and D-S belief combination rules. System control is accomplished using a discrete rule-based control component and uncertain input and output are performed through an interactive belief interface system called IBIS. Each of these features is reviewed. Finally, a simple but detailed example of an application of a frame network expert system is provided. The FRO system user's documentation is provided in the appendix. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

Advances in multiscale methods are presented from two perspectives which address the issue of computational complexity of optimizing and inverse analyzing nonlinear composite materials and structures at multiple scales. The optimization algorithm provides several solutions to meet the enormous computational challenge of optimizing nonlinear structures at multiple scales including: (i) enhanced sampling procedure that provides superior performance of the well-known ant colony optimization algorithm, (ii) a mapping-based meshing of a representative volume element that unlike unstructured meshing permits sensitivity analysis on coarse meshes, and (iii) a multilevel optimization procedure that takes advantage of possible weak coupling of certain scales. We demonstrate the proposed optimization procedure on elastic and inelastic laminated plates involving three scales. We also present an adaptive variant of the measure-theoretic approach (MTA) for stochastic characterization of micromechanical properties based on the observations of quantities of interest at the coarse (macro) scale. The salient features of the proposed nonintrusive stochastic inverse solver are: identification of a nearly optimal sampling domain using enhanced ant colony optimization algorithm for multiscale problems, incremental Latin-hypercube sampling method, adaptive discretization of the parameter and observation spaces, and adaptive selection of number of samples. A complete test data of the TORAY T700GC-12K-31E and epoxy #2510 material system from the NIAR report is employed to characterize and validate the proposed adaptive nonintrusive stochastic inverse algorithm for various unnotched and open-hole laminates. Advances in Multiscale methods also provides us a unique tool to study and analyze human bones, which can be seen as a composite material, too. We used two multiscale approaches for fracture analysis of full scale femur. The two approaches are the reduced order homogenization (ROH) and the novel accelerated reduced order homogenization (AROH). The AROH is based on utilizing ROH calibrated to limited data as a training tool to calibrate a simpler, single-scale anisotropic damage model. For bone tissue orientation, we take advantage of so-called Wolff’s law. The meso-phase properties are identified from the least square minimization of error between the overall cortical and trabecular bone properties and those predicted from the homogenization. The overall elastic and inelastic properties of the cortical and trabecular bone microstructure are derived from bone density that can be estimated from the Hounsfield units (HU). For model validation, we conduct ROH and AROH simulations of full scale finite element model of femur created from the QCT and compare the simulation results with available experimental data.

This dissertation investigates the problem of uncertainty in complex ecological models. The term "complex" is used to convey both the common and scientific meanings. Increasingly, ecological models have become complex because they are more complicated; ecological models are generally multi-variate and multi-leveled in structure. Many ecological models are complex because they simulate the dynamics of complex systems. As a result, and as science moves from the modern/normal to postmodern/post-normal paradigm view of the world, the definition of uncertainty and the problem of uncertainty estimation in models tread the lines between the technical and the philosophical. With this in mind, I have chosen to examine uncertainty from several perspectives and under the premise that the needs and goals of uncertainty estimation, like ecological models themselves, are evolving. Each chapter represents a specific treatment of uncertainty and introduces new methodologies to evaluate the nature, source, and significance of model uncertainty. In the second chapter, 'Determining the significance of threshold values uncertainty in rule-based classification models', I present a sensitivity analysis methodology to determine the significance of uncertainty in spatially-explicit rule-based classification models. In the third chapter, 'Process level sensitivity analysis for complex ecological models', I present a sensitivity analysis methodology at the process level, to determine the sensitivity of a model to variations in the processes it describes. In the fourth chapter, 'A Component Based Approach for the Development of Ecological Simulations', investigate how the process of developing an ecological simulation can be advanced by using component-based simulation frameworks. I conclude with reflection on the future of modeling and studies of uncertainty. / Graduation date: 2003

The problem of handling dependent evidence is an important practical issue for applications of reasoning with uncertainty in artificial intelligence. The existing solutions to the problem are not satisfactory because of their ad hoc nature, complexities, or limitations. In this dissertation, we develop a general framework that can be used for extending the leading uncertainty calculi to allow the combining of dependent evidence. The leading calculi are the Shafer Theory of Evidence and Odds-likelihood-ratio formulation of Bayes Theory. This framework overcomes some of the disadvantages of existing approaches. Dependence among evidence from dependent sources is assigned dependence parameters which weight the shared portion of evidence. This view of dependence leads to a Decomposition-Combination method for combining bodies of dependent evidence. Two algorithms based on this method, one for merging, the other for pooling a sequence of dependent evidence, are developed. An experiment in soybean disease diagnosis is described for demonstrating the correctness and applicability of these methods in a domain of the real world application. As a potential application of these methods, a model of an automatic decision maker for distributed multi-expert systems is proposed. This model is a solution to the difficult problem of non-independence of experts. / Graduation date: 1991