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 [27]. 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 [16], 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.

- STANDARD BAYESIAN NETWORKS
- QUASI-BAYESIAN THEORY AND POLYTOPIC CREDAL SETS
- COMBINING LOCAL INFORMATION

© Fabio Cozman[Send Mail?]

Fri May 30 15:55:18 EDT 1997