[SciPy-User] estimating cov_x matrix with leastsq, without doing a fit.

[josef.pktd at gmail.com]

On Thu, Feb 27, 2014 at 2:03 AM, Andrew Nelson <andyfaff at gmail.com> wrote:
> Dear list,
> I have a least squares data fitting system.  I use two different ways
> of fitting the data; the first is with a differential evolution
> algorithm, the second is with the scipy.optimize.leastsq function.
>
> When I use the leastsq function I obtain the cov_x matrix, giving me
> estimated parameter uncertainties.
>
> However, with my home rolled DE algorithm I don't get a covariance
> matrix and wish to estimate one.  However, I don't want to change the
> fitted parameters, I just want the covariance matrix estimated.  Is
> there any way of getting leastsq to give me the covariance matrix
> solely based on the initial parameters?

If your own fitted parameters also solve the leastsq problem, then
calling leastsq with your values as starting values should not change
the parameters.

>
> If there isn't, can anyone suggest the best way for me to accomplish
> this?  At the moment I am using numdifftools to calculate the Hessian
> and inverting this, but this is not giving me the same numbers as I
> get out of the leastsq function.

Depending on how "nice" your function is, the values can differ quite
a bit depending on the choice of the stepsize in the numerical
derivatives.

In general I would trust numdifftools more than the derivatives
returned by leastsq. You could also compare with the numerical
derivatives in statsmodels.
http://statsmodels.sourceforge.net/devel/tools.html#numerical-differentiation

Josef


>
> regards,
> Andrew.
>
> --
> _____________________________________
> Dr. Andrew Nelson
>
>
> _____________________________________
> _______________________________________________
> SciPy-User mailing list
> SciPy-User at scipy.org
> http://mail.scipy.org/mailman/listinfo/scipy-user