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Inconsistency of Bayesian Inference for ...

Grünwald, Peter...

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Inconsistency of Bayesian Inference for Misspecified Linear Models, and a Proposal for Repairing It by Grünwald, Peter ( Author )

Content Provider	Lemonjar Open Access
Publisher	Australian National University
Publication Date	06-09-2023
Summary	We empirically show that Bayesian inference can be inconsistent under misspecification in simple linear regression problems, both in a model averaging/selection and in a Bayesian ridge regression setting. We use the standard linear model, which assumes homoskedasticity, whereas the data are heteroskedastic, and observe that the posterior puts its mass on ever more high-dimensional models as the sample size increases. To remedy the problem, we equip the likelihood in Bayes' theorem with an exponent called the learning rate, and we propose the Safe Bayesian method to learn the learning rate from the data. SafeBayes tends to select small learning rates as soon the standard posterior is not `cumulatively concentrated', and its results on our data are quite encouraging.
ISBN	-
Item Type	Article
File Type	pdf
File Size	29.34 KB
Language	English
Subjects	-
Unlimited	MYR 0.01
Total read	-
URL	http://arxiv.org/abs/1412.3730

Citation

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AMA 11th EditionReferences

Grünwald, Peter. Inconsistency of Bayesian Inference for Misspecified Linear Models, and a Proposal for Repairing It. Australian National University. September 06, 2023. Accessed November 01, 2024. https://online.provdatabase.com/cite/24043

APA 7th EditionReferences

Grünwald, Peter. (2023). Inconsistency of Bayesian Inference for Misspecified Linear Models, and a Proposal for Repairing It. Australian National University. https://online.provdatabase.com/cite/24043

Chicago 17th EditionReferences

Grünwald, Peter. Inconsistency of Bayesian Inference for Misspecified Linear Models, and a Proposal for Repairing It. Australian National University. 2023. https://online.provdatabase.com/cite/24043

HarvardReferences

Grünwald, Peter. (2023). Inconsistency of Bayesian Inference for Misspecified Linear Models, and a Proposal for Repairing It. [Online]. Australian National University. Available from: https://online.provdatabase.com/cite/24043. (Accessed 01 November 2024).

Harvard AustraliaReferences

Grünwald, Peter, 2023, Inconsistency of Bayesian Inference for Misspecified Linear Models, and a Proposal for Repairing It, Australian National University, viewed 01 November 2024, <https://online.provdatabase.com/cite/24043>

MLA 9th EditionWorks Cited

Grünwald, Peter. Inconsistency of Bayesian Inference for Misspecified Linear Models, and a Proposal for Repairing It. Australian National University, 2023. PROV Database, https://online.provdatabase.com/cite/24043.

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