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

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...

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Bibliographic Details
Published in:Computational statistics 2021-06, Vol.36 (2), p.1243-1261
Main Authors: Bürkner, Paul-Christian, Gabry, Jonah, Vehtari, Aki
Format: Article
Language:English
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
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Summary: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.
ISSN:0943-4062
1613-9658
DOI:10.1007/s00180-020-01045-4