Gaussian conjugacy for a normal linear model
= Gaussian conjugacy for a normal linear model
{c}
If $Y\mid\beta\sim N(X\beta,\Sigma_e)$ and $\beta\sim N(m_0,\Sigma_0)$, then the posterior is normal with <precision matrix> $X^T\Sigma_e^{-1}X+\Sigma_0^{-1}$ and mean equal to the inverse precision times $X^T\Sigma_e^{-1}Y+\Sigma_0^{-1}m_0$.