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Probabilistic Reasoning in Intelligent Systems by Judea Pearl

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4.4.2 The Method of Conditioning (Reasoning by Assumptions)

Conditioning is based on our ability to change the connectivity of a network and render it singly connected by instantiating a selected group of variables. In Figure 4.23, for example, instantiating A to any value would block the pathway B—A—C and would render the rest of the network singly connected, so that the propagation techniques of Section 4.3 would be applicable. Thus, if we wish to propagate the impact of an observed fact, say E = 1, to the entire network, we first assume A = 0 (as in Figure 4.28a), propagate the impact of +e to the variables B, C, and D, repeat the propagation under the assumption A = 1 (as in Figure 4.28b), and finally, average the two results weighted ...

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