Add ZeroSumNormal example notebook

[derwells]

Summary

This PR adds a comprehensive example notebook demonstrating PyMC's ZeroSumNormal distribution, which is ideal for categorical regression with sum-to-zero constraints.

What this notebook covers:

• Identifiability Problems: Why sum-to-zero constraints are needed when modeling categorical predictors
• Design Matrix Analysis: How design matrices create linear dependence with one-hot encoding
• Contrast Coding Schemes: Comparison of reference coding vs sum-to-zero coding with trade-offs
• ZeroSumNormal Mathematics: The covariance structure and properties of the ZeroSumNormal distribution
• Practical Example: Complete worked example comparing treatment group means with posterior analysis
• Advanced Usage: Multi-dimensional sum-to-zero constraints for factorial designs

Background

This continues the work started in #210 by @drbenvincent and @aseyboldt. The original PR from 2021 used PyMC3 with a custom ZeroSumNormal implementation. Since PyMC v4.2.2 (Oct 2022), pm.ZeroSumNormal is available natively, making this much simpler.

I've completely rewritten the notebook for modern PyMC v5, focusing on:

1. Clear pedagogical progression from problem → solution
2. Mathematical foundations with worked examples
3. Visual comparisons between approaches
4. Following all pymc-examples style conventions

Checklist

• Notebook runs sequentially with fresh kernel
• Uses RANDOM_SEED for reproducibility
• ArviZ dark grid style
• Retina figures
• MyST frontmatter with tags, categories, author
• Watermark cell
• Page footer include
• References original PR WIP ZeroSumNormal example notebook #210

Target column in tracker

Done - This is a complete, new notebook using PyMC v5 best practices.

Closes #210

🤖 Generated with Claude Code

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