tulpa_reloo: Selective refit of high-Pareto-k observations (reloo)

In tulpa: Templated Unified Library for Posterior Approximation in Bayesian Hierarchical Models

Selective refit of high-Pareto-k observations (reloo)

Description

PSIS-LOO with exact refits where the importance sampling is unreliable: observations whose Pareto k-hat exceeds k_threshold are re-scored by refitting the model without that observation (through the fit's stored tulpa() call, as in tulpa_kfold()) and evaluating the exact held-out log predictive density. All other observations keep their PSIS-LOO value, so the cost is one refit per flagged observation rather than per fold.

The same restrictions as tulpa_kfold() apply: fixed-effect / GLMM fits only (subsetting breaks a spatial / temporal field), and held-out random-effect groups contribute at their prior mean.

Usage

tulpa_reloo(
  object,
  data,
  k_threshold = .nl_diag("k_usable"),
  n_trials = NULL,
  ndraws = NULL
)

Arguments

object	A tulpa_fit fitted through tulpa() (must carry ⁠$call⁠).
data	The data frame the model was fit to.
k_threshold	Pareto k-hat above which an observation is refit (default 0.7, the standard PSIS reliability gate).
n_trials	Optional binomial denominators (length nrow(data)); defaults to the trials stored on the fit, else 1.
ndraws	Number of posterior draws used for the PSIS-LOO baseline (defaults to all stored draws, or 400 on the draw-free Laplace tier).

Value

A list with elpd_loo (corrected), se_elpd_loo, looic, pointwise (per-observation elpd, exact at the refit observations), reloo_idx (indices refit), pareto_k (the original k-hat values), and k_threshold.

See Also

tulpa_kfold() for the full refit-CV; tulpa_criteria() for PSIS-LOO / WAIC without refits.

Examples

set.seed(1)
d <- data.frame(x = rnorm(120))
d$y <- rpois(120, exp(0.4 + 0.6 * d$x))
fit <- tulpa(y ~ x, data = d, family = "poisson", mode = "laplace")
rl  <- tulpa_reloo(fit, data = d)
rl$elpd_loo

tulpa documentation built on Oct. 19, 2026, 5:09 p.m.