Conditional regression coefficients from a Gaussian precision matrix
= Conditional regression coefficients from a Gaussian precision matrix
{title2=$\theta_{jk}=-\Omega_{jk}/\Omega_{kk}$}
In a <Gaussian graphical model>, regressing component $k$ on the others gives the displayed coefficients, residual variance $1/\Omega_{kk}$ and intercept $\mu_k-\mu_{-k}^{\mathsf T}\theta_{-k,k}$. Opposite directions have identical zero patterns and signs because $\Omega$ is symmetric with positive diagonal, but generally unequal coefficient magnitudes.