Q: In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
The belief network is a well-known graphi cal structure for representing independences in a joint probability distribution. The meth ods, which perform probabilistic inference in belief networks, often treat the conditional probabilities which are stored in the network as certain values. However, if one takes ei ther a subjectivistic or a limiting frequency approach to probability, one can never be certain of probability values. An algorithm should not only be capable of reporting the probabilities of the alternatives of remain ing nodes when other nodes are instanti ated; it should also be capable of reporting the uncertainty in these probabilities relative to the uncertainty in the probabilities which are stored in the network. In this paper a method for determining the variances in in ferred probabilities is obtained under the as sumption that a posterior distribution on the uncertainty variables can be approximated by the prior distribution. It is shown that this assumption is plausible if their is a reason able amount of confidence in the probabili ties which are stored in the network. Fur thermore in this paper, a surprising upper bound for the prior variances in the proba bilities of the alternatives of all nodes is ob tained in the case where the probability dis tributions of the probabilities of the alterna tives are beta distributions. It is shown that the prior variance in the probability at an al ternative of a node is bounded above by the largest variance in an element of the condi tional probability distribution for that node.
A:
Investigation of Variances in Belief Networks