Mathematical Sciences: Computing Environments for Graphical Models

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Graphical models can be defined as statistical models structured in terms of conditional independencies. These models are particularly successful in representing expert systems. This research will develop Bayesian methodology including elicitation of informative prior distributions, model updating and expression of model uncertainty for expert systems and some generalized applications. Expert systems, which are computer programs which mimic human experts, have found both commercial and scientific research application over the last decade. Their actual use in some areas has been limited because of the high level of uncertainty problem solvers must deal with in problematic areas. A rigorous probabilistic basis for expressing uncertainty can be incor- porated into these systems which will allow automated modifica- tion of the system in response to new information.