Gaussian sampling from a precision Cholesky factor
= Gaussian sampling from a precision Cholesky factor
{c}
{title2=$Z=m+L^{-T}\xi$}
If a <positive-definite matrix> $Q=LL^T$ is the <precision matrix> of a <multivariate normal distribution>, draw independent $\xi\sim N(0,I)$ and solve $L^T\eta=\xi$. Then $m+\eta$ has covariance $L^{-T}L^{-1}=Q^{-1}$. This avoids forming the inverse and exploits a banded <Cholesky decomposition> when $Q$ is banded.