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 . Third, we may be interested in abstracting away parts of a model and assessing the effects of this abstraction [7, 18]. For example, in the model of Figure 1, an agent may want to assess the impact of the link between variables A and B, or the impact of merging variables C and D into a single variable.
Figure: Abstraction in Bayesian networks
Our approach to assessment of robustness is to employ convex sets of distributions to represent perturbations in probabilistic models, both in the prior and conditional distributions. The goal of robustness analysis is to study the impact of such perturbations to posterior values; this is done by analyzing bounds of posterior probabilities.
We use the term Quasi-Bayesian theory, as suggested by Giron and Rios , to refer to the theory of convex sets of distributions. In this theory there is no commitment to a underlying ``true'' distribution; a rational decision maker is expected to represent beliefs and preferences through convex sets of distributions which can have more than one element. The basic results of Quasi-Bayesian theory are presented in subsection 2.2. Subsection 2.3 defines two approaches for combination of local information, both of which are studied in this paper.
Fri May 30 15:55:18 EDT 1997