Question: Consider the family of linear Gaussian networks as illustrated

Consider the family of linear Gaussian networks, as illustrated.
a. In a two-variable network, let X1 he the parent of X2, let X1 have a Gaussian prior, and let P (X2, X1) be a linear Gaussian distribution. Show that the joint distribution P(X1, X2) is a multivariate Gaussian, and calculate its covariance matrix.
b. Prove by induction that the joint distribution for a general linear Gaussian network on X1..., Xn, is also a multivariate Gaussian.

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  • CreatedFebruary 14, 2011
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