Partial information use in uncertainty quantification
Zhang, Jianzhong (2006) Partial information use in uncertainty quantification. PhD thesis, Iowa State University.
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Uncertainty exists frequently in our knowledge of the real world. Two forms of uncertainty are considered. One is variability coming from stochasticity. The other is epistemic uncertainty, also called 2nd order uncertainty and other names as well. Often it comes from ignorance or imprecision. In principle, this kind of uncertainty can be reduced by additional empirical data. Stochasticity is well studied in the field of probability theory. A variety of methods have been developed to address epistemic uncertainty. Some of these approaches are confidence limits, discrete convolutions, probabilistic arithmetic, Monte Carlo simulation,copulas, stochastic dominance, clouds, and distribution envelope determination. Belief and plausibility curves, upper and lower previsions, left and right envelopes and probability boxes designate an important type of representation for bounded uncertainty about distribution. Some methods combine probability theory and interval mathematics. Intervals have the potential for bounding the result of an operation. Discretization error coming from discretizing distributions may be bounded by intervals. Distribution envelope determination (DEnv) uses interval based analysis. If the dependency is not specified, result bounds will include the entire range of possible dependencies. These bounds will be wider than if a particular dependency is specified. I have worked on new algorithms to process the dependency relationships. Pearson correlation can be used to improve the results, for example. Also partial dependence information might be available in the form of unimodality or of probability over a specified area of a joint distribution. If this information is used in the calculation, more accurate results can be obtained than that without using this information.Another situation is uncertainty about the parameters of a distribution. All these topics are researched in this work. They are implemented in the software we call Statool. Based on the developed methods, uncertainty can be flexibly considered and added into models. This can make the model closer to real situations. One problem posed by Sandia National Laboratory is studied in this work. Other applications include Pert networks, decision models and others.
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