Math behind uncertainty of constraint parameters

[mbakker7]

One of the cool features of LMFit is that parameters can have a min and max value, even when doing Levenberg-Marquardt optimization.
In the manual of older versions of LMFit, there was quite some math explaining how the uncertainty of these parameters was computed when the parameter was constraint by a min and max value. I could not find this math back in the current manual. Is that still there? And if it is not, is the old math still accessible somewhere?

[newville]

@mbakker7 See https://lmfit.github.io/lmfit-py/bounds.html for the explanation and

lmfit-py/lmfit/parameter.py

Line 893 in 776e14d

def setup_bounds(self):

(and also the following scale_gradient method for the code that implements this.

[mbakker7]

Thanks, @newville , but I seem to recall from the old manual that you included an analysis with derivatives to explain how the covariance is "re-transformed" to estimate the uncertainties of the original un-transformed parameters. Do I recall that correctly, and if so, is that analysis still available somewhere?

[newville]

@mbakker7 Maybe https://github.com/lmfit/lmfit-py/blob/master/lmfit/minimizer.py#L761

in which Parameter.scale_gradient is doing most of the heavy lifting. I don't we removed anything like that from the documentation. Maybe that was in the documentation for leastsqbound, which is where we got some of the original ideas for the covariance transformation.

[mbakker7]

My memory is probably bad, but I am giving it a last try. Do you happen to have a pdf of version 0.8 or 0.9? I'd love to take a look at those. I tried to re-generate those from the repositories, but that turns out not to be so easy.

[newville]

No, I do not. The GitHub repo will go back that far, and you are welcome to browse the older versions of the codes and documentation all you want. I can not provide any more help than that.

[mbakker7]

I really appreciate your help. Thanks for a great package.