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

Uppsala universitet, Statistiska institutionen Aalto Univ, Dept Comp Sci, Espoo, Finland Aalto Univ, Dept Comp Sci, Espoo, Finland 2023

Sivula, Tuomas
Magnusson, Måns
Vehtari, Aki

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.

Bayesian computation; leave-one-out cross-validation; uncertainty; variance estimator; bias; Probability Theory and Statistics; Sannolikhetsteori och statistik; Article in journal; info:eu-repo/semantics/article; text

10.1080.03610926.2021.2021240

English

UPE oai:DiVA.org:uu-511323
0000-0002-0296-2719
0000-0003-2164-9469
doi:10.1080/03610926.2021.2021240
ISI:000750786600001
1399993843

UPPSALA UNIV LIBR
From OAIster®, provided by the OCLC Cooperative.

edsoai.on1399993843