RE: FOCE objective function
From: "LSEN (Lars Erichsen)" <lsen@novonordisk.com>
Subject: RE: [NMusers] FOCE objective function
Date: Tue, 13 Nov 2001 12:47:41 +0100
In the usual Laplace approximation of the integral,
the first derivative of the exponent is 0 in etahat,
because etahat maximises the exponent. This is not assumed in
the derivation in the NONMEM manual Part VII on page 4 which is why
the last term is not zero.
The integral is L=Int[exp(-0.5*(Phi(eta)+eta'*O*eta))]
where O=inverse of Omega
If etahat minimises Phi(eta)+eta'*O*eta
we have that (Gamma=derivative of Phi):
Gamma(etahat)+2*O*etahat=0, so that
0.5*Gamma(etahat)+O*etahat=0.
I hope this is of use.
Lars Erichsen
Pharmacokinetics, Pharmacometrics
Novo Nordisk
Denmark.