Update confidence.rst

[skoldobskiy]

Hello!
I found a bug in an example with calculating c.i.
The assessment of sigma's and related plotting of confidence intervals performed with sqrt(chi2/redchi), however, it should be sqrt((chi2-chi2.min)/redchi). The updated equation provides accurate and adequate contour plots for parameter uncertainties.

Also renaming dchi2 to chi2 can be considered.

Description

https://lmfit.github.io/lmfit-py/confidence.html#lmfit.conf_interval2d -- no ellipses are plotted here, however, they should. The proposed change corrects this.

no no

Type of Changes

• [ x] Bug fix
• New feature
• Refactoring / maintenance
• Documentation / examples

Tested on

Verification

Have you

• included docstrings that follow PEP 257?

• referenced existing Issue and/or provided relevant link to mailing list?

• verified that existing tests pass locally?

• verified that the documentation builds locally?

• squashed/minimized your commits and written descriptive commit messages?

• added or updated existing tests to cover the changes?
• updated the documentation and/or added an entry to the release notes (doc/whatsnew.rst)?
• added an example?

[newville]

@skoldobskiy Ah, good catch. We do that subtraction with conf_interval2d(....., chi2_out=False) but not with
conf_interval2d(....., chi2_out=True). I guess it is easier to change the doc than the code, especially because chi2.min() is sometimes an interesting thing to know.

So, I'm +1 on this change. I'll leave this open for a couple of days in case there are any objections or other considerations. But, I hope to merge this and #941 and then be ready to push a release soonish.

[skoldobskiy]

@newville Also I propose that the doc [https://lmfit.github.io/lmfit-py/confidence.html#lmfit.conf_interval2d] can be changed in a way to emphasize that conf_interval2d studies the ellipses of standard errors, not those obtained by conf_interval(out, out, sigmas=sigma_levels) (if I understood the procedures correctly).
Currently, this is not clear to the reader/user and very similar naming can be a reason of misinterpretation.

[newville]

@skoldobskiy If you have wording there that you want to change, are you willing to include that in this PR? I would say "please do!"

[skoldobskiy]

1. I found that https://lmfit.github.io/lmfit-py/examples/documentation/confidence_chi2_maps.html#sphx-glr-examples-documentation-confidence-chi2-maps-py is corrected already. I updated my old version with this example to synchronize them.
2. I also have added a couple of sentences in the confidence interval discussion -- for clarification. However I would like if somebody can check that I am fully correct

[newville]

@skoldobskiy it looks like there are some RST formatting issues - like single quotes where you might want double backticks. Have you installed and run "pre-commit"? That might help identify those issues.

[reneeotten]

please use a formatting string

[skoldobskiy]

@newville @reneeotten Ok thanks, I'll check and fix it.

[newville]

@skoldobskiy Thanks -- this looks okay to me. @reneeotten any objection from anyone to Squash+Merge? If I don't hear otherwise, I will plan to do that on Monday.

[newville]

@skoldobskiy @reneeotten Thanks!