Update the log_phi prior mean from method-of-moments estimates

Estimates \(\phi\) from each dataset individually using moment-based approximations (the same approach used in check 1 of pre_inference_checks()), then overwrites log_phi_mean in stan_data with the log of the median implied \(\phi\) across all datasets.

This replaces the fixed distribution-specific default with a value anchored to the actual data scale, which is particularly useful for the gamma distribution: the default prior mean (shape ≈ 12) can be far above the data-implied shape (typically 2–8 for incubation periods), causing gamma_lccdf to evaluate to log(0) = -Inf during Stan's initialisation phase.

log_phi_sd is left unchanged so the prior remains diffuse around the data-derived centre.

Usage

update_phi_prior(stan_data, datasets)

Arguments

stan_data: A named list returned by prepare_stan_data_from_datasets().
datasets: The same named list of datasets passed to prepare_stan_data_from_datasets(). Used only for moment calculations.

Value

stan_data with log_phi_mean replaced by log(median(implied_phi)). All other fields are unchanged. If no finite implied-\(\phi\) values can be derived, a warning is issued and stan_data is returned unmodified.

Details

Moment approximations per distribution:

lognormal: \(\phi = \log(1 + (\mathrm{sd}/\mathrm{mean})^2)\) (approximate log-variance)
gamma: \(\phi = (\mathrm{mean}/\mathrm{sd})^2\) (method-of-moments shape)
Weibull: \(\phi\) solved numerically from the CV via \(CV^2 = \Gamma(1+2/k)/\Gamma(1+1/k)^2 - 1\)

For datasets that report only median + IQR, the SD is approximated as \((Q3-Q1)/1.35\); for median + range, as \((\max-\min)/4\); for frequency tables, the weighted SD of the (mid-)points is used.

Examples

if (FALSE) { # \dontrun{
  stan_data <- prepare_stan_data_from_datasets(datasets_Mpox, dist_type = 2)
  stan_data <- update_phi_prior(stan_data, datasets_Mpox)
  fit <- rstan::sampling(stan_model, data = stan_data, chains = 4, iter = 2000)
} # }