Simple kriging

For known zero mean, invertible observation covariance $\Sigma$, target covariance vector $c$ and target variance $v_0$, simple kriging predicts $c^T{\Sigma }^{-1}z$ with error variance $v_0-c^T{\Sigma }^{-1}c$. Completing the covariance quadratic form proves optimality. A multivariate normal distribution makes this the exact conditional mean and variance.