NNGP Laplace at given hyperparameters — laplace_gp

Single-point Laplace approximation for a Matern/exponential GP spatial field at fixed (sigma2_gp, phi_gp). Used by dispatch_laplace_spatial when spatial$type == "gp". The neighbor structure is read straight off the validated spec – call validate_gp(spatial, data) first if constructing manually.

Usage

laplace_gp_at(
  y,
  n_trials,
  X,
  spatial,
  family = "binomial",
  phi = 1,
  sigma2_gp = NULL,
  phi_gp = NULL,
  re_idx = NULL,
  n_re_groups = 0L,
  sigma_re = 1,
  max_iter = 100L,
  tol = 1e-06,
  n_threads = 1L,
  offset = NULL,
  weights = NULL
)

Arguments

y: Response vector.
n_trials: Trial sizes (binomial).
X: Fixed-effects design matrix.
spatial: A tulpa_gp spec, validated (i.e., neighbor_info populated).
family: Distribution family.
phi: Dispersion passed to the family, held fixed. One convention at every door: for gaussian / lognormal this is the residual VARIANCE (the SD is sqrt(phi)), for neg_binomial_2 the size, gamma the shape, beta the precision, t the scale; binomial and poisson ignore it. The compiled kernels parameterize the two variance families by the residual SD and are handed sqrt(phi) at the boundary.
sigma2_gp: Marginal variance (NULL -> 1.0).
phi_gp: Range / decay parameter (NULL -> 1.0).
max_iter: Newton iterations.
tol: Newton tolerance.
n_threads: OpenMP threads.
weights: Optional per-observation likelihood weights (length length(y)), scaling each row's log-density, score and Fisher curvature.

Value

The raw cpp_laplace_fit_gp result list, augmented with sigma2_gp, phi_gp, and the spatial spec.