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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| Published in | Computational statistics Vol. 36; no. 2; pp. 1243 - 1261 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.06.2021
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0943-4062 1613-9658 |
| DOI | 10.1007/s00180-020-01045-4 |
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| 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
distribution on the outcome values. We demonstrate the method using lagged simultaneously autoregressive (SAR) models as a case study. |
|---|---|
| AbstractList | 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. 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. 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. |
| Author | Gabry, Jonah Bürkner, Paul-Christian Vehtari, Aki |
| Author_xml | – sequence: 1 givenname: Paul-Christian orcidid: 0000-0001-5765-8995 surname: Bürkner fullname: Bürkner, Paul-Christian email: paul.buerkner@gmail.com organization: Department of Computer Science, Aalto University – sequence: 2 givenname: Jonah surname: Gabry fullname: Gabry, Jonah organization: Applied Statistics Center and ISERP, Columbia University – sequence: 3 givenname: Aki surname: Vehtari fullname: Vehtari, Aki organization: Department of Computer Science, Aalto University |
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| SubjectTerms | 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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| Title | Efficient leave-one-out cross-validation for Bayesian non-factorized normal and Student-t models |
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