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The author’s past work in this area has shown that the probability of a state of a Bayesian network, found using the standard Bayesian techniques, could be equated to the Maximum Entropy solution and that this result enabled us to find minimally prejudiced estimates of missing information in Bayesian networks. In this paper we show that in the class of Bayesian networks known as Bayesian trees, we are able to determine missing constraint values optimally using only the maximum entropy formalism. Bayesian networks that are specified entirely within the maximum entropy formalism, whether or not information is missing, are called generalized Bayesian networks. It is expected that further work will fully generalize this result. © 2006 American Institute of Physics [ABSTRACT FROM AUTHOR]

Intelligent systems based on Bayesian networks have been successful in medical diagnosis, finance and many other areas. Updating probabilities in Bayesian networks relies on algorithms that require complete causal information. Sensitivity analysis now strongly indicates that probabilities in Bayesian networks are not robust and this reinforces the view that a sound theoretical model for finding a minimally prejudiced estimate of the prior distribution is desirable. In this paper we are concerned with how to find the optimum prior distribution, given all and only the knowledge available. In particular, we show how to integrate prior knowledge expressed in terms of inequality constraints, into a Bayesian network based intelligent system. © 2005 American Institute of Physics [ABSTRACT FROM AUTHOR]