loglik_niche_math_ncst_r: Reference (pure-R) negative log-likelihood for the NCST...

In xnicher: Estimates Ecological Niche Models Using Ellipses

Reference (pure-R) negative log-likelihood for the NCST density

Description

Evaluates the Non-Central Skew t (NCST) negative log-likelihood using pure base-R arithmetic (no C++ calls except for the C-vine Cholesky). This is the Stage 1 reference implementation following the SSDLC: correctness is everything, speed is irrelevant.

Usage

loglik_niche_math_ncst_r(theta, env_occ, eta = 1)

Arguments

theta	Numeric vector of length 3*p + p*(p-1)/2 + 1: [xi(p), log_sigma(p), v(n_v), alpha(p), log_r(1)].
env_occ	Numeric matrix (n x p) of occurrence data.
eta	Scalar shape parameter for the C-vine prior (default 1).

Details

The NCST stochastic form (Hasan & Chen 2025, Definition 1) is: T = X / sqrt(Y / r), X ~ SN_k(xi, Omega, alpha), Y ~ chi^2_r, where the location xi enters INSIDE the skew-normal BEFORE chi-squared scaling. This differs from Azzalini/Branco & Dey's skew-t where location is added AFTER scaling.

Value

Scalar negative log-likelihood (same constant-dropping convention as the C++ kernel).

References

Hasan, M. R. & Chen, M.-H. (2025). Flexible Modeling of Multivariate Skewed and Heavy-Tailed Data via a Non-Central Skew t Distribution. arXiv:2507.10465v1.

xnicher documentation built on Sept. 15, 2026, 5:08 p.m.