Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC

TL;DR

This paper introduces efficient, stable methods for Bayesian model evaluation using leave-one-out cross-validation and WAIC, leveraging Pareto-smoothed importance sampling to improve robustness and computational speed.

Contribution

It presents a fast, stable computational approach for LOO and WAIC using existing posterior simulations, including a new importance sampling regularization technique.

Findings

PSIS-LOO is more robust than traditional methods in finite samples.

The methods provide approximate standard errors for predictive accuracy estimates.

Implementation in the 'loo' R package facilitates practical application.

Abstract

Leave-one-out cross-validation (LOO) and the widely applicable information criterion (WAIC) are methods for estimating pointwise out-of-sample prediction accuracy from a fitted Bayesian model using the log-likelihood evaluated at the posterior simulations of the parameter values. LOO and WAIC have various advantages over simpler estimates of predictive error such as AIC and DIC but are less used in practice because they involve additional computational steps. Here we lay out fast and stable computations for LOO and WAIC that can be performed using existing simulation draws. We introduce an efficient computation of LOO using Pareto-smoothed importance sampling (PSIS), a new procedure for regularizing importance weights. Although WAIC is asymptotically equal to LOO, we demonstrate that PSIS-LOO is more robust in the finite case with weak priors or influential observations. As a byproduct of our calculations, we also obtain approximate standard errors for estimated predictive errors and for comparing of predictive errors between two models. We implement the computations in an R package called 'loo' and demonstrate using models fit with the Bayesian inference package Stan.