[Scilab-users] evaluate error on each parameter calculated with leastsq

[Stéphane Mottelet]

Hello,

If you can make the hypothesis that your data is corrupted by gaussian
noise, then you can approximate the covariance matrix of your estimated
parameters. Let p be the vector of parameters and r(p) the residual vector
given by

r(p)=sigma^(-1)*(y-Y(p))

where y is your measuement vector, Y(p) the "simulated" measurement, sigma
a diagonal matrix with the std error for each measurement. If we denote by

drdp(p) the derivative (or jacobian matrix) of r with respect to p then the
covariance matrice C of parameters can be estimated by


C=F^(-1)

where

F=drdp(p)' * drdp(p)

is the Fisher information matrix. The diagonal terms of V give you the
variance of the parameters. Of course, even in the gaussian case, this is a
crude approximation.... Here is (attached) a simple example where the
derivative is approximated with the "derivative" macro of Scilab.



S.


2014-02-19 14:31 GMT+01:00 Yohann <yohann.morille at univ-angers.fr>:

> Hi Antoine,
> thank you for your answer but
> what I need is a confidence interval on each parameter !
> Cheers
> Yohann
>
>
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