Weakly-informative priors for occupancy Laplace fits

Constructs a prior specification consumed by tobs() when a Laplace method (method = "laplace" etc.) is used for the occupancy family. The penalty is applied as a quadratic term + sum((beta_j - mu_j)^2 / (2 * sd_j^2)) added to the negative-log-posterior in each M-step submodel block by tulpa::tulpa_laplace() (via the per-block beta_prior).

Usage

occu_priors(
  p_intercept = list(mean = 0, sd = 1.5),
  p_slope = list(mean = 0, sd = 2.5),
  beta_occ_intercept = list(mean = 0, sd = 2),
  beta_occ_slope = list(mean = 0, sd = 5)
)

Arguments

p_intercept

Prior on the detection intercept (logit scale). A list list(mean = numeric(1), sd = numeric(1)). Default list(mean = 0, sd = 1.5).

p_slope

Prior on detection slopes (every non-intercept detection coefficient). Default list(mean = 0, sd = 2.5).

beta_occ_intercept

Prior on the occupancy (psi / psi1) intercept. Default list(mean = 0, sd = 2).

beta_occ_slope

Prior on occupancy slopes. Default list(mean = 0, sd = 5).

Value

An occu_priors object, ready to pass to tobs(..., priors = ...).

Details

The defaults are weakly informative: they pull the detection intercept toward p = 0.5 strongly enough to break the psi-p identifiability ridge at small J, but stay wide enough not to bias estimates at N >= 600 with informative covariates. Setting any sd to Inf disables that component of the prior (same penalised objective, just 1/Inf^2 = 0).

Examples

# disable the detection-slope penalty
priors <- occu_priors(p_slope = list(mean = 0, sd = Inf))
priors

# \donttest{
sim <- simulate_occu(N = 100, J = 3, n_occ_covs = 1, n_det_covs = 1,
                     seed = 1)
fit <- tobs(~ occ_cov1, data = sim$data, family = occu(),
            detection = ~ det_cov1, y = sim$y, method = "laplace",
            priors = occu_priors(),
            control = list(verbose = FALSE, progress = FALSE))
coef(fit)
# }