Fit a tobs model with Laplace approximation (internal)

Uses tulpa's generic EM+Laplace engine (tulpa::tulpa_em_laplace()) with occupancy-specific E-step and M-step encoding, augmented with a weakly-informative quadratic prior on the fixed-effect coefficients (see occu_priors()). The prior is attached to each M-step block as a per-block beta_prior (see .attach_priors_to_blocks() in R/occu_priors.R), which tulpa threads through every phase – the EM iterations and the MI / Gibbs correction refits alike. Supports all built-in model types. Called from .tobs_fit_model(); not user-facing.

Usage

.tobs_laplace(
  model,
  spatial = NULL,
  re = NULL,
  priors = NULL,
  sigma_beta = 10,
  max_iter = 50L,
  tol = 1e-04,
  damping = 0.3,
  correction = c("auto", "mi", "gibbs", "none"),
  n_imputations = 20L,
  n_gibbs = 10L,
  seed = NULL,
  approx = c("gaussian_laplace", "simplified_laplace"),
  re_aghq = TRUE,
  n_quad = 9L,
  lkj_eta = 1.5,
  latent_prior = NULL,
  heldout_state = NULL,
  verbose = TRUE
)

Arguments

model

A tobs_model from .tobs_build_model().

spatial

Optional tobs_spatial spec (NULL for non-spatial).

priors

Optional prior spec from occu_priors(). NULL -> use the package defaults. Pass FALSE (or "none") to disable the prior and recover the historical unpenalised MAP behavior – the penalised objective is Q(beta) = -log L(beta) + sum (beta_j - mu_j)^2 / (2 sd_j^2), so sd_j = Inf yields a zero penalty term.

sigma_beta

Reserved for future use (NUTS-side beta prior); ignored by the EM-Laplace path.

max_iter, tol, damping

EM controls.

correction

Post-EM correction ("none", "mi", "gibbs"). MI / Gibbs run tulpa's post-EM Rubin-pooled correction; the fixed-effect prior (when active) threads into the correction refits, so the corrected fit is penalised the same way as the EM point estimate.

n_imputations

Number of MI draws when correction = "mi".

verbose

Print per-iteration progress.