Abstract
Bayesian belief networks provide estimates of conditional probabilities, called query responses. The precision of these estimates is assessed using posterior distributions. This paper discusses two claims and a conjecture by Kleiter (1996) concerning the exact posterior distribution of queries. The two claims provide conditions where a query has an exact beta distribution. The first claim is clarified by the following generalization. Assuming a BDe prior and complete data, a query has the same distribution under equivalent network structures. If the query can be represented as a network parameter under an equivalent structure, it must then have a beta distribution. Kleiter's second claim is contradicted by a counter-example. His conjecture, concerning finite mixtures of beta distributions, is also disproved.
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