[SciPy-User] confidence interval for leastsq fit

[josef.pktd at gmail.com]

On Thu, Apr 28, 2011 at 8:11 AM, Till Stensitzki <mail.till at gmx.de> wrote:
> In ultrafast physics, we often use, that the ration of the reduced chi^2
> follows a  F-Distribution. Most of the time, we are a fitting a sum-of-
> exponentials model to our data, in which the covariance between the
> parameters is quite hight. Using the cov-diagonal to calculate the
> confidence interval underestimates the size and form of the interval, so we are
> using a exhaustive search method.
>
> See
>
> http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1260379/?page=4

interesting, it sounds similar to profile log-likelihood, which I
haven't quite figured out yet how to program efficiently, but I have
never seen it in the least-squares context.

In the profile loglikelihood discussion the emphasis is on the
non-linearity and not so much on multi-collinearity.
If there is strong correlation between parameter estimates then it
should also blow up the covariance matrix (similar to a near singular
Hessian) and the standard errors, I think.

But I guess multi-collinearity can have an even more drastic effect in
non-linear models than in the linear model.

Josef

>
> for details.
>
>
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