gminus2-statistical-engine

This release provides the first complete implementation of a 2D statistical engine for inference in the ((\mu, \kappa)) parameter space, combining Gaussian likelihoods with a non‑Gaussian, bounded nuisance prior. The engine is fully vectorized in JAX and includes both frequentist and Bayesian inference pipelines. Core features Gaussian likelihood model for (\Delta a_\mu) with explicit nuisance shift (\kappa). Non‑Gaussian, bounded mixture prior for (\kappa), implemented in closed form and fully JAX‑compatible. Grid‑based inference in ((\mu, \kappa)) with: profile likelihood (q(\mu)) Bayesian marginal posterior (p(\mu)) Wilks theorem diagnostics via pseudo‑experiments, sampling nuisance parameters from the prior and computing empirical (q)-distributions. JAX‑accelerated vectorization for likelihood evaluation, marginalization, and toy generation. Reference plotting scripts for profile likelihood, Bayesian posterior comparison, and Wilks CDF validation. Purpose This release establishes a clean, reproducible baseline for studying non‑Gaussian nuisance effects, Wilks breakdown, and hybrid frequentist–Bayesian inference in low‑dimensional physics‑motivated models.