This paper provides a general purpose search-based technique for computing posterior probabilities in arbitrary discrete Bayesian Networks. This is an ``anytime'' algorithm, that at any stage can estimate prior and posterior probabilities with a known error bound. It is shown how well it works for systems that have normality conditions that dominate the probabilities, as is the case in many diagnostic situations where we are diagnosing systems that work most of the time, and for commonsense reasoning tasks where normality assumptions (allegedly) dominate. We give a characterisation of those cases where it works well, and discuss how well it can be expected to work on average. Finally we give a discussion on a range of implementations, and discuss why some promising approaches do not work as well as may be expected.
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