= Gaussian conditional variance from precision
{c}
{title2=$\operatorname{Var}(X_i\mid X_{-i})=1/\Omega_{ii}$}
For a nonsingular <multivariate normal distribution> with <precision matrix> $\Omega$, fixing all coordinates except $X_i$ leaves a density proportional to $\exp[-\Omega_{ii}(x_i-m_i)^2/2]$ after completing the square. Thus its <conditional variance> is the reciprocal diagonal precision entry. This is conditioning on every other coordinate, not the marginal <variance> $(\Omega^{-1})_{ii}$.
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