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Probabilistic Reasoning in Intelligent Systems by Judea Pearl

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4.3 BELIEF PROPAGATION IN CAUSAL POLYTREES (SINGLY CONNECTED NETWORKS)

The tree structures treated in the preceding section require that exactly one variable be considered a cause of another given variable. This restriction simplifies computations, but its representational power is rather limited, since it forces us to form a single node from all causes sharing a common consequence. By contrast, when people see many potential causes for a given observation, they weigh one cause against another as independent variables, each pointing to a specialized area of knowledge. As an illustration, consider the situation discussed in Example 7 of Chapter 2:

Mr. Holmes receives a phone call at work from his neighbor notifying him that she heard a burglar ...

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