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

2015/07/31 by Aki Vehtari, Andrew Gelman, Jonah Gabry · 1 voice · 267 citations
Computer Science · Engineering · Mathematics · #Fault Detection and Control Systems #Gaussian Processes and Bayesian Inference #Statistical Methods and Inference #stat.CO #stat.ME

paper · pdf · doi:10.1007/s11222-016-9696-4

published as Statistics and Computing, 2017, Volume 27, Issue 5, pp 1413-1432

openalex created_date 2016/06/24 · openalex publication_date 2016/08/30 · arxiv created 2016/09/12 · arxiv updated 2017/12/18 · openalex updated_date 2026/08/02

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.

Citations

• A Predictive Approach to Model Selection
• A survey of cross-validation procedures for model selection
• Strictly Proper Scoring Rules, Prediction, and Estimation
• Asymptotic Equivalence of Bayes Cross Validation and Widely Applicable Information Criterion in Singular Learning Theory

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Discussions

• Yes. I have seen this used in the context leave-one-out cross-validation (LOO CV), taking the LOO posterior predictive distribution to be compared against the observation in P-P and Q-Q plots in Vetha [bsky, 0 points, 0 comments]

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