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

Author

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  • Paul-Christian Bürkner

    (Aalto University)

  • Jonah Gabry

    (Columbia University)

  • Aki Vehtari

    (Aalto University)

Abstract

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- $$t$$ t distribution on the outcome values. We demonstrate the method using lagged simultaneously autoregressive (SAR) models as a case study.

Suggested Citation

  • Paul-Christian Bürkner & Jonah Gabry & Aki Vehtari, 2021. "Efficient leave-one-out cross-validation for Bayesian non-factorized normal and Student-t models," Computational Statistics, Springer, vol. 36(2), pages 1243-1261, June.
    • Handle: RePEc:spr:compst:v:36:y:2021:i:2:d:10.1007_s00180-020-01045-4
    DOI: 10.1007/s00180-020-01045-4
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