Multinomial Polya node

[ismailsenoz]

Description

This PR implements the Multinomial-Polya node using Polya-Gamma augmentation for inference. The implementation includes:

• Polya-Gamma augmented inference for the multinomial likelihood
• Logistic stick-breaking transformation for probability simplex parameterization
• Support for both analytical expectations and Monte Carlo sampling for omega parameters
• Efficient computation of natural parameters for the likelihood

[codecov]

Codecov Report

Attention: Patch coverage is 92.30769% with 5 lines in your changes missing coverage. Please review.

Project coverage is 74.63%. Comparing base (b88de4d) to head (fcd0193).
Report is 38 commits behind head on main.

Files with missing lines	Patch %	Lines
src/nodes/predefined/multinomial_polya.jl	93.87%	3 Missing ⚠️
src/rules/multinomial_polya/psi.jl	83.33%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #445      +/-   ##
==========================================
+ Coverage   74.42%   74.63%   +0.20%     
==========================================
  Files         195      198       +3     
  Lines        5623     5688      +65     
==========================================
+ Hits         4185     4245      +60     
- Misses       1438     1443       +5     

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