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

[Samuel Gougeon]

Le 19/02/2014 14:31, Yohann a écrit :
> Hi Antoine,
> thank you for your answer but
> what I need is a confidence interval on each parameter !
A raw empirical approach:
Let R be the RMS residue for the best set P of fitting parameters.
* change the value of P(1) by -- say -- +1%, for the parameter #1.
* calculate the new residue R1p, and the change dR1p = abs(R-R1p)
    you may symmetrize the process : change P(1) => P(1)*0.99 (-1%)
    calculate R1m with this biased fitting model, and get dR1=dR1m+dR1p
* These dR somewhat represent sensitivities of the fit w.r.t. to each 
parameter.
* Assume that the confidence interval for parameter # is proportional to 
1/dR#

For "stiff" parameters, dR# will be big (easily divergent), and 1/dR# small.

DISCLAIMER : You may use this approach under your own responsability ;)
Its main (may be unique) merit is to be simple.

Samuel