Efficient leave-one-out cross-validation for Bayesian non-factorized normal and Student-t models

• Published in: Computational statistics Vol. 36; no. 2; pp. 1243 - 1261
• Main Authors: Bürkner, Paul-Christian, Gabry, Jonah, Vehtari, Aki
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2021; Springer Nature B.V
• Subjects: Autoregressive models; Bayesian analysis; Economic Theory/Quantitative Economics/Mathematical Methods; Mathematics and Statistics; Model accuracy; Original Paper; Probability and Statistics in Computer Science; Probability Theory and Stochastic Processes; Statistics; Non-factorized models; Bayesian inference; SAR models; Cross-validation; Pareto-smoothed importance-sampling
• ISSN: 0943-4062; 1613-9658
• DOI: 10.1007/s00180-020-01045-4

Cross-validation can be used to measure a model’s predictive accuracy for the purpose of model comparison, averaging, or selection. Standard leave-one-out cross-validation (LOO-CV) requires that the observation model can be factorized into simple terms, but a lot of important models in temporal and spatial statistics do not have this property or are inefficient or unstable when forced into a factorized form. We derive how to efficiently compute and validate both exact and approximate LOO-CV for any Bayesian non-factorized model with a multivariate normal or Student- t distribution on the outcome values. We demonstrate the method using lagged simultaneously autoregressive (SAR) models as a case study.