Design sensitivity function ($d(x,\xi )=f(x{)}^{T}M(\xi {)}^{-1}f(x)$)

The sensitivity function is the normalized variance of a fitted regression mean. Its average under the design is the number $p$ of model coefficients, since $\int dd\xi =\mathrm{tr}(M^{-1}M)=p$. The directional derivative of $\log \det M$ towards a point mass at $x$ is $d(x,\xi )-p$.