In the real world we can rarely meet all the assumptions of a Bayesian model. First, we have to face imperfections in an agent's beliefs, either because the agent had no time, resources, patience, or confidence to provide exact probability values. Second, we may deal with a group of disagreeing experts, each specifying a particular distribution [Levi1980, Seidenfeld & Schervish1990]. Third, we may be interested in abstracting away parts of a model and assessing the effects of this abstraction [Chrisman1996a, Ha & Haddawy1996].
Figure 1: Abstraction in Bayesian networks: elimination of weak links and grouping of variables.
To emphasize the relationship between abstraction and robustness analysis, suppose a decision-maker is contemplating a situation with several hundred variables. For a particular inference, some variables may minimally affect the probabilities of interest. In Figure 1, node A and its ancestors weakly affect node B, and node C and D can be collapsed into a single node. The original model is abstracted by breaking links and grouping nodes. Now the decision-maker can use robustness analysis to determine bounds on the posterior quantities in the abstracted model. Large bounds indicate poor performance and suggest reevaluation of the abstraction procedure.
Tue Jan 21 15:59:56 EST 1997