say we have a multivariate normal distribution with ${\boldsymbol Y} \sim \mathcal{N}(\boldsymbol\mu, \Sigma)$

The conditional expection is $\overline{\boldsymbol\mu}=\boldsymbol\mu_1+\Sigma_{12}{\Sigma_{22}}^{-1}({\boldsymbol a}-\boldsymbol\mu_2)$

Is this saying that for each value of $a$ in a dataset you minus the mean and multiply by the covariance matrices to obtain the conditional expectation or is it a double summation of $ a - \boldsymbol\mu_2$? I am slightly confused as to what the terms actually are and how to calculate them.

  • $\begingroup$ @Xi'an Hi, thanks for link. I think I understand. So it is the sub matrices multiplying these values? $\endgroup$
    – JB191
    Apr 17 '21 at 12:37