[FEATURE] Add BART prior sampling convenience functions and vignette (RFC 0003)

[andrewherren]

Summary

Add sampleBARTPrior() (R) and sample_bart_prior() (Python) as convenience wrappers for sampling from the BART prior, along with a vignette demonstrating their use.

Depends on

#329 — the observation weights argument must be available first.

Motivation

Sampling from the BART prior is a standard Bayesian workflow step useful for:

1. Prior calibration — understanding what functions BART places non-negligible probability on before seeing data, to guide hyperparameter choice (num_trees, alpha, beta, leaf scale)
2. Prior predictive checks — generating data from p(y | X, prior) to verify the prior isn't ruling out plausible outcomes
3. Pedagogy — showing new users what BART "believes" before data is observed

Approach

Running BART with all-zero observation weights produces exact prior draws:

• Split evaluation reduces to the tree structure prior ratio (data have no effect)
• Leaf parameters are drawn from their prior N(0, σ²_μ)
• σ² samples from its IG prior

The convenience functions wrap this pattern so users don't need to understand the mechanics:

# R
sampleBARTPrior(X, num_samples = 100, mean_forest_params = list(num_trees = 50))

# Python
sample_bart_prior(X, num_samples=100, mean_forest_params={"num_trees": 50})

Scope

• sampleBARTPrior() in R/bart.R, exported from NAMESPACE
• sample_bart_prior() in stochtree/bart.py, exported from __init__.py
• Both hard-code num_gfr = 0 (GFR initialization is data-dependent and ill-defined with zero weights); emit a warning if the user passes num_gfr > 0 with zero weights manually
• Vignette demonstrating prior draws, prior predictive distributions, and a simple calibration example
• Unit test verifying that marginal variance of prior draws matches num_trees * leaf_scale² for a flat leaf prior
• sample_sigma2_global should default to TRUE/True in the convenience wrapper so users can easily construct the full prior predictive y ~ N(f(x), σ²)

Future work

• After completing and validating this prior sampler, add the same functionality for BCF models

Reference

RFC 0003: https://github.com/StochasticTree/rfcs/blob/main/0003-bart-prior-sampling.md