Robust Bayesian analysis is a field with clear practical relevance; applications of Bayesian networks must determine the relationship between the accuracy of probability values and the accuracy of inferences. Yet research on Bayesian networks has not fully explored this aspect of inference, mostly due to the difficulty of handling probability intervals. Theories of inference that are restricted to linear bounds or belief functions have been plagued by serious mathematical and philosophical difficulties.
The algorithms presented here change dramatically this situation. First, we use Quasi-Bayesian theory, which has a solid, axiomatic foundation, with well-defined analogies for conditioning and decision making. Second, we establish algorithms for general exact and approximate robust inferences. We expect our results to bring robustness analysis to the forefront of tools that are used in a daily basis by Bayesian analysts. However, several issues remain to be addressed. It is necessary to evaluate which algorithms work best with empirical data; a comparison of integer programming methods  with interior-point methods is particularly important. Finally, and perhaps most importantly, methods to elicit information about credal sets from experts should be created and evaluated; for example, there must be guidance on how to select between natural extension/type-1 combinations.
Fri May 30 15:55:18 EDT 1997