[Scilab-users] leastsq question : what is 'gopt' useful for?

[Stéphane Mottelet]

Hello,

Le 22/03/2016 10:41, antoine.monmayrant at laas.fr a écrit :
> Hi everyone,
>
> I have a very general and naive question concerning leastsq: what am I 
> to do with "gopt", the "gradient of f at xopt"?
>
> Is there a way to link it to the confidence interval for each 
> parameter of my fit?
Not really, but since leastsq is a wrapper for optim, which returns the 
gradient at returned "optimal" solution, it is also returned. However, 
if the final gradient is seen to be far from the zero vector, then all 
confidence intervals based on the inverse of the Fisher matrix (computed 
with the Jacobian) will not have any sense, since these "linear" 
statistics are based on a development where the first term (using the 
gradient) is supposed to vanish... Hence, having access to the final 
gradient can be of interest.
> For the moment, I know how to estimate these confidence intervals when 
> I have access to the Jacobian matrix of my fit function.
> Could "gopt" be of some use to estimate the confidence intervals when 
> the Jacobian matrix is not known?
no, but you can approximate your Jacobian with "numderivative"

S.
> If not, what can we use it for?
>
> Cheers,
>
>
> Antoine
>
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Département de Génie Informatique
EA 4297 Transformations Intégrées de la Matière Renouvelable
Université de Technologie de Compiègne -  CS 60319
60203 Compiègne cedex