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

[Antoine Monmayrant]

Le 03/22/2016 10:55 AM, Stéphane Mottelet a écrit :
> 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.

Ah, OK it makes sense, thanks Stéphane!

>> 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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