Mathematical Sciences: Computing Environments for Graphical Models

图形模型可以定义为根据条件独立性构建的统计模型。这些模型在表示专家系统方面特别成功。本研究将发展贝叶斯方法，包括信息先验分布的推导、模型更新和专家系统模型不确定性的表达，以及一些广义应用。专家系统是一种模仿人类专家的计算机程序，在过去十年中在商业和科学研究中都有应用。它们在某些领域的实际使用受到限制，因为问题解决者必须在有问题的领域处理高度的不确定性。可以在这些系统中加入表达不确定性的严格概率基础，从而允许对系统进行自动修改，以响应新的信息。

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.