Probabilistic reasoning in expert systems: theory and alogorithms
Addresses the use probability theory as a tool for designing with and implementing uncertainity reasoning. Provides many concrete algorithms, explores techniques for solving multimembership classification problems not based directly on causal networks, and offers practical recommendations, matching specific methods with sample expert systems.
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GRAPH THEORETIC CONSIDERATIONS
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7r messages 7r value abductive inference algorithm alternatives arcs assigned assume assumption axioms of probability belief burglarized causal network cause chain chapter Clq2 Clqj coin compute conditional distributions conditional independencies conditional probability contains d-separated DAG in Figure defined diagnostic problem discussed disease envelope equal equipossible event example exclusive and exhaustive expert systems explanation set EXPLANATION.LIST fill-in graph in Figure HBEST implies independent given inference network influence diagram initial instantiated variables joint distribution large numbers Lemma Let G maximum cardinality search Mises network in Figure obtained operative formula ordering P(ai P(di P(Ei parents patient Pearl possible values principle of indifference priori probabilities prob probabilistic probability propagation probability space probability theory probability values probable explanation Proof propositional variables random relative frequencies rule sequence singly connected subjectivist subset Suppose toss tree of cliques triangulated graph uncertainty undirected graph updating variables given vertex vertices