Driankov, D. (1986). Inference with Consistent Probabilities in Expert Systems. Technical Report LiTH-IDA-R-86-12, Department of Computer and Information Science, Linköping University, Sweden. Also in Proc. of IJCAI-87. (bibtex),
Abstract: The objective of the present paper is twofold: first, to provide an algorithm which helps in eliciting consistent, with respect to the axioms of the probability theory, a priori and conditional probabilities as well as higher order conditional and joint probabilities for a set of events representing pieces of evidence and hypotheses in the context of a rule based expert system. The algorithm proposed, utilizes the least possible number of a priori and conditional probabilities as input in order to obtain all the remaining ones and then, proceeds further by producing the lower and upper bounds for particular higher order conditional and joint probabilities so that these be consistent with the input provided. In the case, when inconsistent lower and upper bounds are obtained, it is shown how the latter can be turned into consistent ones by changing the values of only these input-probabilities which are directly representing the higher order probability expressions under consideration.Secondly, a number of typical cases with respect to the problems of aggregation and propagation of uncertainty in expert systems is presented and it is shown how these can be modelled using the results of the algorithm proposed. For this purpose no global assumptions for independence of evidence and for mutual exclusiveness of hypotheses are required since the presence of independent and/or dependent pieces of evidence as well as the presence of mutually exclusive hypotheses is explicitly encoded in the input-probabilities and thus, such a presence is automatically taken care of by the algorithm when obtaining higher order probabilities.
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