= Gaussian Bayesian network
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A Gaussian Bayesian network specifies a linear normal conditional model at each node of a <Bayesian network>: $X_j\mid X_{\operatorname{pa}(j)}\sim N(\alpha_j+\gamma_j^TX_{\operatorname{pa}(j)},\sigma_j^2)$. <Independent> local errors and an acyclic ordering generate a joint <multivariate normal distribution>. Positive conditional <variances> give a nonsingular joint <multivariate normal distribution>. The graph constrains <regression coefficients> and hence <conditional independence>.
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