Conditional Independence

Part of the Oberwolfach Seminars book series (OWS, volume 39)


Conditional independence constraints are simple and intuitive restrictions on probability distributions that express the notion that two sets of random variables are unrelated, typically given knowledge of the values of a third set of random variables. A conditional independence model is a family of probability distributions that satisfy a collection of conditional independence constraints. In this chapter we explore the algebraic structure of conditional independence models in the case of discrete or jointly Gaussian random variables. Conditional independence models defined by graphs, known as graphical models, are given particular emphasis. Undirected graphical models are also known as Markov random fields, whereas directed graphical models are often termed Bayesian networks.


Direct Acyclic Graph Conditional Independence Markov Property Pairwise Constraint Chain Graph 
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© Birkhäuser Verlag AG 2009

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