Gaussian conditional expectation
= Gaussian conditional expectation
{c}
For jointly Gaussian $(S,Y)$ with $\operatorname{cov}(S)=V$,
$$
\mathbb E[Y\mid S]=\mathbb EY+\operatorname{cov}(Y,S)V^{-1}(S-\mathbb ES).
$$
= Gaussian conditional expectation
{c}
For jointly Gaussian $(S,Y)$ with $\operatorname{cov}(S)=V$,
$$
\mathbb E[Y\mid S]=\mathbb EY+\operatorname{cov}(Y,S)V^{-1}(S-\mathbb ES).
$$