Introduction to Graphical Models
نویسنده
چکیده
Two real-valued or vector-valued random variables X, Y are independent for probability measure P (written: X ⊥ Y [P ]) if for all sets A and B, P[X ∈ A, Y ∈ B] = P[X ∈ A] · P[Y ∈ B]. For jointly discrete or jointly continuous random variables this is equivalent to factoring of the joint probability mass function or probability density function, respectively. The variables X and Y are conditionally independent given a third random variable Z for probability distribution P (written: X ⊥ Y | Z [P ]) if the conditional pmf or pdf factors1 in the form: p(x, y | z) = p(x | z) p(y | z). This relation arises frequently in Bayesian analysis and computation; we now explore it further. For nice discussions of conditional independence in statistical inference see (Dawid 1979a,b, 1980) and for a more advanced view (Dawid and Lauritzen 1993).
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