On the third line, we incorrectly state that
$\Delta p = \sum H^{-1} \left(\nabla T \frac{\partial W}{\partial p}\right)^T (T(x) - I(W(x; p)))$
It should be
$\Delta p = H^{-1} \sum \left(\nabla T \frac{\partial W}{\partial p} \right)^T (T(W(x;0)) - I(W(x; p)))$
Why is $H^{-1}$ inside the summation for expression of $\Delta p$?
It could be either inside or outside of the summation (numerically identical), but I agree it would be clearer if it were on the outside.
On the third line, we incorrectly state that
$\Delta p = \sum H^{-1} \left(\nabla T \frac{\partial W}{\partial p}\right)^T (T(x) - I(W(x; p)))$
It should be
$\Delta p = H^{-1} \sum \left(\nabla T \frac{\partial W}{\partial p} \right)^T (T(W(x;0)) - I(W(x; p)))$
Why is $H^{-1}$ inside the summation for expression of $\Delta p$?
It could be either inside or outside of the summation (numerically identical), but I agree it would be clearer if it were on the outside.