feat #7713: implement ICARRV/CARRV as SymbolicRVs

[asifzubair]

Description

We will implement ICARRV and CARRV as SymbolicRVs by subclassing SymbolicMVNormalUsedInternally. This will eliminate the need for rng_fn.

Related Issue

• Closes Add rng_fn to CAR/ICAR #7713
• Related to #

Checklist

• Checked that the pre-commit linting/style checks pass
• Included tests that prove the fix is effective or that the new feature works
• Added necessary documentation (docstrings and/or example notebooks)
• If you are a pro: each commit corresponds to a relevant logical change

Type of change

• New feature / enhancement
• Bug fix
• Documentation
• Maintenance
• Other (please specify):

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📚 Documentation preview 📚: https://pymc--7879.org.readthedocs.build/en/7879/

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 92.95%. Comparing base (58b49f2) to head (0fbccf4).
⚠️ Report is 3 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #7879   +/-   ##
=======================================
  Coverage   92.94%   92.95%           
=======================================
  Files         116      116           
  Lines       18845    18857   +12     
=======================================
+ Hits        17516    17528   +12     
  Misses       1329     1329           

Files with missing lines	Coverage Δ
pymc/distributions/multivariate.py	93.98% <100.00%> (+0.07%)	⬆️

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[asifzubair]

Hi @jessegrabowski , could you please give this a review when you have a moment ? Thank you 🙏

[asifzubair]

Hi @ricardoV94 , sorry, was wondering if you could offer some comments, will get me unstuck. Thank you 🙏

[ricardoV94]

I left a comment in #7713 (comment)

I don't have enough knowledge to say whether we should add this feature

[ColtAllen]

Hey @asifzubair, resharing the link @ricardoV94 shared on improper distribution sampling.

Are you able to add a test to meet @jessegrabowski's criteria?

To merge the PR, I would want to see that the prior and the no-data MCMC gives the same answer

@theorashid feel free to comment. Given these challenges of improper priors, do you think ICAR is better left to the wonderful world of INLA?