SPDE Laplace at given hyperparameters — laplace_spde

Single-point Laplace approximation for an SPDE spatial field at a fixed (range, sigma). Used by both dispatch_laplace_spatial (single-point path) and fit_spde (single-point branch) so the call site stays a single source of truth.

Usage

laplace_spde_at(
  y,
  n_trials,
  X,
  spatial,
  family = "binomial",
  phi = 1,
  range = NULL,
  sigma = 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_spatial object of type "spde".
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.
range: Spatial range (NULL -> use spatial$prior_range[1]).
sigma: Marginal SD (NULL -> use spatial$prior_sigma[1]).
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_spde result list (mode, log_det_Q, log_marginal, n_iter, converged), augmented with range, sigma, and the spatial spec for downstream prediction.