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Unbiased estimator for the variance of the leave-one-out cross-validation estimator for a Bayesian normal model with fixed variance

Author

Listed:
  • Tuomas Sivula
  • Måns Magnusson
  • Aki Vehtari

Abstract

When evaluating and comparing models using leave-one-out cross-validation (LOO-CV), the uncertainty of the estimate is typically assessed using the variance of the sampling distribution. Considering the uncertainty is important, as the variability of the estimate can be high in some cases. Previous studies show that no general unbiased variance estimator can be constructed, that would apply for any utility or loss measure and any model. We show that it is possible to construct an unbiased estimator considering a specific predictive performance measure and model. We demonstrate an unbiased sampling distribution variance estimator for the Bayesian normal model with fixed model variance using the expected log pointwise predictive density (elpd) utility score. This example demonstrates that it is possible to obtain improved, problem-specific, unbiased estimators for assessing the uncertainty in LOO-CV estimation.

Suggested Citation

  • Tuomas Sivula & Måns Magnusson & Aki Vehtari, 2023. "Unbiased estimator for the variance of the leave-one-out cross-validation estimator for a Bayesian normal model with fixed variance," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 52(16), pages 5877-5899, August.
  • Handle: RePEc:taf:lstaxx:v:52:y:2023:i:16:p:5877-5899
    DOI: 10.1080/03610926.2021.2021240
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