Internal function for converting parameters to natural parameters.

Preprocessing before generating a dist_spec: converts a distribution's parameters to its natural parameters via the per-type to_natural() method, re-attaching uncertainty where parameters are uncertain.

When any of the supplied parameters are uncertain the uncertainty is propagated to the natural parameters using a first-order (delta-method) approximation. The uncertain parameters are treated as independent normals; the natural parameters are evaluated at their means and their variances are obtained from the Jacobian of the transformation, computed by central finite differences. Each natural parameter is returned as a Normal() with that mean and standard deviation.

Usage

convert_to_natural(x)

Arguments

x

A <dist_spec>.

Value

A named list of natural parameters.

Residual limitation

The delta method represents each natural parameter's marginal uncertainty but discards the correlation between natural parameters induced by the shared unnatural parameters (for example, shape and rate of a gamma both depend on the uncertain mean). Specify the distribution directly in terms of its natural parameters when that correlation matters.