Maximum-likelihood fit for ECORR

[abhisrkckl]

• Enables maximum-likelihood fitting for ECORR parameters when time-correlated noise components are absent.
• Only available in DowhillGLSFitter.
• Also works in pintk
• Fitting for time-correlated noise components is too slow at the moment. (May come back to this later).
• Added an example notebook for noise fitting.

[codecov]

Codecov Report

Attention: 62 lines in your changes are missing coverage. Please review.

Comparison is base (602cfba) 68.78% compared to head (fd05c72) 68.76%.
Report is 1 commits behind head on master.

Files	Patch %	Lines
src/pint/residuals.py	55.46%	46 Missing and 7 partials ⚠️
src/pint/models/timing_model.py	63.63%	5 Missing and 3 partials ⚠️
src/pint/utils.py	95.45%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #1673      +/-   ##
==========================================
- Coverage   68.78%   68.76%   -0.03%     
==========================================
  Files         105      105              
  Lines       24556    24630      +74     
  Branches     4401     4401              
==========================================
+ Hits        16892    16936      +44     
- Misses       6555     6589      +34     
+ Partials     1109     1105       -4     

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[abhisrkckl]

I have given up on implementing the ecorr derivatives for the time being. The fitting works fine without them, albeit slower (but not prohibitively so). I'll come back to this after finishing the paper.

[abhisrkckl]

One more simulated example:

The corner plot is from ENTERPRISE analysis.
Blue "truth" lines represent the injected values.
Red error bar plots represent the PINT maximum-likelihood estimates.

[abhisrkckl]

https://nanograv-pint--1673.org.readthedocs.build/en/1673/examples/noise-fitting-example.html

[dlakaplan]

The results look reasonable, although I haven't been able to check over the new code line-by-line.

[dlakaplan]

While I didn't look line-by-line, I can merge this if you want. It shouldn't hurt anything existing and more use might exposure any issues (or it might just be a great new feature).

[abhisrkckl]

Yes. Please merge this.

[dlakaplan]

I think there is an issue with the ephemeris hosted at NANOGrav (@JPGlaser ). Probably we can ignore this?

[abhisrkckl]

Yes. I reran the failed ephemeris_connection tests, but they failed again. I think we can ignore that.