Make concentration in NegativeBinomialObservation a RandomVariable

[damonbayer]

Closes #178.
Partially addresses #198.

I now also estimate the overdipsersion parameter in hospital_admissions_model.qmd.
This makes the inference take quite a while, so maybe we should look at reducing the scope of that tutorial.
It leads to a nice-looking posterior predictive:

But funky looking posterior latent infections:

Not sure if this is just an artifact of the hdi plots or if it indicates something undesirable about the model.

[codecov]

Codecov Report

Attention: Patch coverage is 93.75000% with 1 line in your changes missing coverage. Please review.

Project coverage is 92.80%. Comparing base (0219353) to head (0446afd).

Files	Patch %	Lines
model/src/pyrenew/observation/poisson.py	83.33%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #267      +/-   ##
==========================================
+ Coverage   92.73%   92.80%   +0.06%     
==========================================
  Files          40       40              
  Lines         909      903       -6     
==========================================
- Hits          843      838       -5     
+ Misses         66       65       -1     

Flag	Coverage Δ
unittests	92.80% <93.75%> (+0.06%)	⬆️

Flags with carried forward coverage won't be shown. Click here to find out more.

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

[sbidari]

@damonbayer did you also look at equal tailed intervals for the posterior latent infection?

[damonbayer]

@damonbayer did you also look at equal tailed intervals for the posterior latent infection?

No. I would accept a PR to add that figure, though :)

[dylanhmorris]

Caught the problem in #269 from looking at the example figures highlighted here by @damonbayer. Suggest landing that first and merging it in here.

[damonbayer]

@dylanhmorris #269 is merged here

[dylanhmorris]

LGTM

[sbidari]

The posterior plots in this tutorial doesn't look right. Looks like the posterior samples are all just same array?

and the diagnostics are bad

[damonbayer]

There is some variability in latent infections (see my original post), but I agree it is strange.

[sbidari]

There is no within chain variability in the posterior samples

[dylanhmorris]

The prior on the concentration is not working as written. I tried swapping in a LogNormal prior and things just worked. Will investigate further.