Transform prior samples to original scale

Generate prior samples and transform them using the same matrix transformation as posterior samples. This is the correct approach for visualizing priors on the original (unscaled) scale, especially for the intercept which depends on contributions from multiple coefficient priors.

transform_prior_samples(
  fit,
  n_samples = 10000,
  seed = NULL,
  formula_scale = NULL
)

Arguments

fit

a fitted model object with prior_list and optionally formula_scale attributes

n_samples

number of samples to generate (default: 10000)

seed

random seed for reproducibility (optional). The caller's random-number state (.Random.seed and RNGkind()) is restored afterwards. With NULL, the caller's random-number stream is used.

formula_scale

optional nested list containing standardization information. If not provided, extracted from fit attribute. An entry must name every predictor that fit standardized for that parameter. The transformation is derived from the fitted structure stored in fit: the fixed-effect design, a log intercept, and the random-effect SD structure.

Value

A matrix of prior samples on the original (unscaled) scale, with columns matching the structure of posterior samples. Columns that are not mapped by the scale transformation, such as the totals and allocation nodes of ordered priors, keep their fitted-scale values.

Details

When models use auto-scaling (standardizing predictors), the posterior samples are on the standardized scale. To correctly visualize priors on the original scale, we cannot simply apply a linear transformation to individual priors because the intercept on the original scale is a weighted sum of multiple priors:

$$\beta_0^{orig} = \beta_0^* - \sum_i \frac{\mu_i}{\sigma_i} \beta_i^*$$

This function generates samples from ALL priors simultaneously and applies the same matrix transformation used for posterior samples, which correctly handles the intercept and all other parameters.

Monitored random-effect nodes that the model defines deterministically from other nodes are computed from the prior draws of those nodes with the model's own definitions: standard deviations derived from a variance allocation (random_variance_allocation()), scalar correlations sampled on the Fisher-z or logit scale, and LKJ Cholesky factors, correlation matrices, and partial correlations. Every parameter-catalog quantity that depends only on such nodes and on the priors can therefore be evaluated on the prior draws (see parameter_draws()). The auxiliary nodes of spike-and-slab and mixture priors are included from the components of their rng() draws: the component indicator (<parameter>_indicator) of both, and the inclusion probability (<parameter>_inclusion) and slab draws (<parameter>_variable) of spike-and-slab priors; the random-number stream of the other columns is unchanged. The totals of ordered priors (<parameter>_ordered_total) are included with the same auxiliary nodes of a spike-and-slab or mixture total; the slices of a spike-and-slab total of an interaction share its inclusion probability and indicator, as in the fitted model. Standardized latent random effects, nodes derived from them, such as realized group coefficients, the component nodes of mixture priors, and the auxiliary nodes of Dirichlet priors are not included, so catalog quantities that depend on them cannot be evaluated on the prior draws. Variance-allocation inclusion indicators are included, drawn from their inclusion probabilities. Valid LKJ concentrations do not guarantee representable primitive Beta draws. Nonfinite draws or draws outside the open interval (0, 1) stop before deterministic replay with BayesTools_lkj_rng_unavailable (parent BayesTools_prior_rng_unavailable). The condition records block, primitive, K, eta, original-row failed_draws and n_failed. Choose a concentration whose primitive draws remain representable; no retry, clamping, endpoint substitution or prior change is performed. Explicit scalar correlation transforms that numerically saturate a boundary retain their compiler refusal rather than changing the requested prior or scale.

Conditions

The conditions of transform_scale_samples() apply (BayesTools_formula_transform_unavailable and BayesTools_refit_required). Expression-point priors without a certified persisted recipe stop with BayesTools_formula_transform_unavailable and reason "uncertified_point_replay"; non-representable LKJ primitive draws signal BayesTools_lkj_rng_unavailable.

See also

transform_scale_samples() plot_posterior()

Examples

# With a fitted model that used formula_scale:
# prior_samples <- transform_prior_samples(fit, n_samples = 10000)
# This can then be used with density() or for custom plotting