Abstract
This paper investigates the problem of belief update in Bayesian networks (BN) with uncertain evidence. Two types of uncertain evidences are identified: virtual evidence (reflecting the uncertainty one has about a reported observation) and soft evidence (reflecting the uncertainty of an event one observes). Each of the two types of evidence has its own characteristics and obeys a belief update rule that is different from hard evidence, and different from each other. The particular emphasis is on belief update with multiple uncertain evidences. Efficient algorithms for BN reasoning with consistent and inconsistent uncertain evidences are developed, and their convergences analyzed. These algorithms can be seen as combining the techniques of traditional BN reasoning, Pearl's virtual evidence method, Jeffrey's rule, and the iterative proportional fitting procedure.
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