loglik_niche_math_presence_only: Negative log-likelihood (presence-only, math scale)

In xnicher: Estimates Ecological Niche Models Using Ellipses

Negative log-likelihood (presence-only, math scale)

Description

Computes the negative log-likelihood of a multivariate normal niche model using only presence records, with no background correction (Jimenez et al. 2019, Eq. 2 without the M-restricted denominator).

Usage

loglik_niche_math_presence_only(theta, env_occ, eta = 1, neg = TRUE, ...)

Arguments

theta	Numeric vector of unconstrained parameters (math scale): [\mu, \log\sigma, v] of length 2p + p(p-1)/2.
env_occ	Data frame or matrix (n \times p) of environmental values at presence points.
eta	Numeric scalar, shape parameter for the LKJ C-vine prior on the correlation matrix (default 1 = uniform over correlations).
neg	Logical. If TRUE (default), returns the negative log-likelihood (suitable for minimisation).
...	Additional arguments (ignored; for compatibility).

Details

The minimised objective is:

-\log\mathcal{L} = \frac{n}{2}\log|\Sigma| + \frac{1}{2}\sum_{i=1}^{n} (\mathbf{x}_i - \mu)^\top \Sigma^{-1}(\mathbf{x}_i - \mu)

The (2\pi) normalisation constant is dropped (does not affect the optimum).

Internally, \Sigma = L L^\top is reconstructed from theta via cvine_cholesky, and the Mahalanobis distances are computed via a triangular solve L^{-1}(\mathbf{x}_i - \mu).

Value

Scalar numeric: the (negative) log-likelihood.

References

Jimenez, L., Soberon, J., Christen, J. A., & Soto, D. (2019). On the problem of modeling a fundamental niche from occurrence data. Ecological Modelling, 397, 109823.

See Also

[optimize_niche()] for multi-start fitting, [loglik_niche_math_cpp()] for the M-restricted model.

Examples

theta <- start_theta(example_env_occ_2d)
ll <- loglik_niche_math_presence_only(theta, example_env_occ_2d)

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