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

Tuomas Sivula, Måns Magnusson, Aki Vehtari

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)

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.
Original languageEnglish
Number of pages24
JournalCommunications in Statistics: Theory and Methods
Early online date12 Jan 2022
DOIs
Publication statusPublished - 3 Feb 2022
MoE publication typeA1 Journal article-refereed

Keywords

  • Bayesian computation
  • leave-one-out cross-validation
  • uncertainty
  • variance estimator
  • bias

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