Probability integral transform from a predictive CDF

The generic, family-agnostic half of a PIT residual check: the model package supplies the posterior-predictive CDF evaluated at each observation (a [n_draws x n_obs] matrix, or a draw-averaged [n_obs] vector), and this returns the PIT value per observation. For a discrete or mixed response (a hurdle has a point mass at zero) supply the left limit cdf_lower (P(Y < y)); the randomized PIT then draws one uniform per observation and interpolates F(y^-) + U (F(y) - F(y^-)), which is uniform under a correct model. With cdf_lower = NULL the response is treated as continuous and the PIT is the draw-averaged CDF.

Usage

tulpa_pit(cdf, cdf_lower = NULL, jitter = TRUE)

Arguments

cdf

Posterior-predictive CDF at the observed value, P(Y <= y). A [n_draws x n_obs] matrix (averaged over draws here) or an [n_obs] vector.

cdf_lower

Optional left-limit CDF P(Y < y), same shape as cdf, for the randomized PIT of a discrete / mixed response.

jitter

If TRUE (default) and cdf_lower is NULL, add a tiny uniform jitter to break ties from a discretized CDF; ignored when cdf_lower is supplied (the interpolation already randomizes).

Value

Numeric vector of length n_obs of PIT values in [0, 1].

See also

tulpa_criteria()