###############################################################################
# Model specifications. This project uses one analysis script per model
# (see <topic>-<variant>.R), so there is no shared brms formula
# registry here. What does live at session start is the custom log-normal
# family in its natural-scale (mean–sd) parameterization: its custom_family()
# object and companion Stan block. custom_family() comes from brms, so this
# file must be sourced after packages.R (init.R guarantees the order). The
# matching log_lik / posterior_predict / posterior_epred helpers are in
# functions.R.
###############################################################################


lognormal_natural <- custom_family(
  name  = "lognormal_natural",
  dpars = c("mu", "sigma"),
  links = c("log", "log"),
  lb    = c(0, 0),
  type  = "real"
)

stan_lognormal_natural <- "
  real lognormal_natural_lpdf(real y, real mu, real sigma) {
    real common_term = log(1+sigma^2/mu^2);
    return lognormal_lpdf(y | log(mu)-common_term/2,
                              sqrt(common_term));
  }
  real lognormal_natural_rng(real mu, real sigma) {
    real common_term = log(1+sigma^2/mu^2);
    return lognormal_rng(log(mu)-common_term/2,
                            sqrt(common_term));
  }
"