Improve horseshoe prior demo: pedagogical visualizations, bug fix, Python 3.12 + CUDA 12 environment

[Copilot]

Summary

This PR improves the horseshoe prior MCMC demo for learners new to Bayesian methods, fixes a code bug in visualization.py, and documents the correct environment setup for Python 3.12 and CUDA 12.

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Bug Fixes

visualization.py — KeyError on inclusion_prob column

The plot_feature_importance function referenced top_features["inclusion_prob"] but get_feature_importance() never produces a column with that name. The column is called beta_inclusion_prob, lambda_inclusion_prob, or combined_inclusion_prob depending on the method argument. Fix: add a method parameter to plot_feature_importance and select the correct column.

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Environment / Dependency Fixes

pyproject.toml

• Added Python 3.12 to the classifiers.
• Tightened lower bounds: jax>=0.7.0, jaxlib>=0.7.0, numpyro>=0.15.0.
  Root cause: JAX 0.10.0 removed jax.extend.core.primitives.xla_pmap_p, which NumPyro ≤ 0.20.1 still imports. JAX 0.7–0.9.x is the correct range for the current NumPyro release.
• Fixed GPU extra from deprecated jax[cuda12_pip] → jax[cuda12].

README.rst

Added an "Environment Setup (Python 3.12 + CUDA 12)" section with step-by-step install commands and a version compatibility note.

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Notebook Improvements (demo/horseshoe_mcmc_feature_selection_demo.ipynb)

Six new sections added to make the demo a self-contained lesson:

New section	What it teaches
1b — Horseshoe prior density	MC-sampled marginal prior density vs Gaussian and Laplace; two-panel plot (broad view + near-zero spike) showing why horseshoe is both sparser and less biased than the Lasso
2 — SNR annotation	Computes signal-to-noise ratio and plots the response distribution so students can assess problem difficulty before fitting
4 — Forest plot	Posterior 94 % credible intervals for all β, colored gold (true signal) vs blue (noise) — the canonical Bayesian coefficient summary
5 — R-hat / ESS explainer + histogram	Markdown table defining R-hat and ESS with thresholds; histogram of R-hat across all β with green/orange/red reference lines
5b — Shrinkage factor κ_j	Scatter + histogram of posterior mean κ_j = 1/(1+τ²λ_j²) split by signal vs noise, directly illustrating the horseshoe mechanism
7b — Exercise A (worked example)	Sweeps scale_global (τ₀) over [0.02, 0.05, 0.1, 0.2, 0.5, 1.0], plots precision/recall/F1 and # selected features vs τ₀ on a log scale with the rule-of-thumb reference line

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Test Results

• 85/85 existing tests pass on Python 3.12.
• Notebook executes end-to-end (all 16 code cells) with zero errors.
• CodeQL security scan: 0 alerts.
• Automated code review: no issues found.