From firstname.lastname@example.org Fri Dec 1 01:09:34 1995
Subject: RESET HESSIAN Dear nonmem user,
Occasionally, during the fitting algorithm of NONMEM, the message "RESET HESSIAN" appears. In theory, at least the way I understand it, it should not matter what the Hessian is during the iterative procedure so long as we are converging towards the solution. What is not clear to me is the following :
1. When and why NONMEM requires to reset the Hessian ?
2. Can the objective function still be used (at least for comparing nested models) ?
3. Are parameter estimates unbiased, and more importantly, are their estimated standard errors reliable, given that the Hessian has been changed.
4. What actions are needed for a subsequent NONMEM run if resetting the Hessian is an unfortunate situation ?
I look forward to hearing from you.
From alison Fri Dec 1 13:24:21 1995
Subject: RESET HESSIAN The Hessian matrix is the second derivative matrix of the objective function. The following message refers to this matrix:
Explanation: The search starts with the Hessian of the pseudo-Newton search set to the identity matrix. It is updated after each iteration, using a rank 1 update procedure. When there is no longer a sensible direction to take, but convergence has not been achieved, this may be due to inadequacy of the updated Hessian. Then the Hessian is reset to a certain positive semi-definite diagonal matrix, and a new direction computed from this matrix (and the gradient vector) is tried.
The appearance of the message indicates why an unusually large number of function evaluations were used for the iteration (extra ones were needed to compute the new Hessian and perform a line search along the new direction) and why an unusually long CPU time was needed for the iteration (if someone is monitoring the intermediate output). Its appearance suggests that the search is not going easily, and perhaps (not necessarily) something is wrong.
A reset indicates some problem during the search. (It indicates that the approximation to the Hessian is no longer acceptable, and must be "recomputed".) The message can be safely ignored, unless more than just a couple of resets occur, or resets occur right before the end of the search, in which case a poor fit (judged by other means) can result, and the user should carefully regard his set-up, and consider possible reasons for why a minimum, let alone one which corresponds to a good estimate, was difficult to find (there can be many possible reasons).
It has nothing to do with statistics per se.