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Probabilistic Reasoning in Intelligent Systems by Judea Pearl

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Chapter 3

MARKOV AND BAYESIAN NETWORKS

Two Graphical Representations of Probabilistic Knowledge

Probability is not really about numbers; it is about the structure of reasoning.— G. Shafer

Probability is not really about numbers; it is about the structure of reasoning.

—G. Shafer

In this chapter, we shall seek effective graphic representations of the dependencies embedded in probabilistic models. First, we will uncover a set of axioms for the probabilistic relation “X is independent of Y, given Z” and offer the set as a formal definition for the notion of informational dependency. Given an initial set of independence relationships, the axioms permit us to infer new independencies by nonnumeric, logical manipulations. Using this axiomatic ...

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