Fix MCMC_walkthrough.ipynb

[dlakaplan]

This notebook runs, although I'm not sure if the results are sensible/as intended.

[dlakaplan]

https://nanograv-pint--1679.org.readthedocs.build/en/1679/examples/MCMC_walkthrough.html

[dlakaplan]

Strangely, when I run it locally I don't get the same errors and I don't get a good phase-o-gram

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Comparison is base (4d07835) 68.42% compared to head (5d5641b) 68.42%.

Additional details and impacted files

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##           master    #1679   +/-   ##
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  Coverage   68.42%   68.42%           
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  Files         104      104           
  Lines       24339    24339           
  Branches     4346     4346           
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  Hits        16653    16653           
  Misses       6599     6599           
  Partials     1087     1087           

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[dlakaplan]

I thought I fixed the second error that appears by the phaseogram, but it's still there in the RTD.

[dlakaplan]

So I fixed the syntax errors and now don't get good phase-o-grams. But at least now I see consistent results.

[dlakaplan]

So I realized that the reason the phaseograms looked bad was because it was replacing F1 with the phase in the fit. It computed:

maxbin, like_start = marginalize_over_phase(
    phases, template, weights=fitter.weights, minimize=True, showplot=True
)
phase = 1.0 - maxbin[0] / float(len(template))

but then set fitvals[-1] equal to that value. So the initial fit position was horrible. As far as I can tell the fit only includes F0 and F1, and I don't understand where the phase comes into it. Maybe @scottransom knows?

[dlakaplan]

Also, the second example discussed using a phase term in the likelihood (and hard a hard bound on the prior for that). But I don't see it in the model. With the phase prior removed it now doesn't give -inf for the likelihood.

[scottransom]

The absolute phase information for the fit used to be tacked on invisibly at the end of the parameter vectors (that's why we loop up to :-1 for regular params). But now absolute phase is handled in PINT. So maybe that needs to be changed now.

[dlakaplan]

The absolute phase information for the fit used to be tacked on invisibly at the end of the parameter vectors (that's why we loop up to :-1 for regular params). But now absolute phase is handled in PINT. So maybe that needs to be changed now.

Do you think that needs to be changed for this notebook? Or maybe we can merge this notebook back in and put in a new issue on adding the phase info back?

[abhisrkckl]

This looks good to me. Shall I merge this?

[dlakaplan]

Yes, please.