On Bayes factors for the linear model
| Autor: | Thomas S. Shively, Stephen G. Walker |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Statistics and Probability
Applied Mathematics General Mathematics Uniformly most powerful test 05 social sciences Linear model Bayes factor 01 natural sciences Agricultural and Biological Sciences (miscellaneous) F-distribution 010104 statistics & probability symbols.namesake 0502 economics and business Prior probability Linear regression symbols Applied mathematics 0101 mathematics Statistics Probability and Uncertainty Invariant (mathematics) General Agricultural and Biological Sciences Elliptical distribution 050205 econometrics Mathematics |
| Zdroj: | Biometrika. 105:739-744 |
| ISSN: | 1464-3510 0006-3444 |
| DOI: | 10.1093/biomet/asy022 |
| Popis: | SummaryWe show that the Bayes factor for testing whether a subset of coefficients are zero in the normal linear regression model gives the uniformly most powerful test amongst the class of invariant tests discussed in Lehmann & Romano (2005) if the prior distributions for the regression coefficients are in a specific class of distributions. The priors in this class can have any elliptical distribution, with a specific scale matrix, for the subset of coefficients that are being tested. We also show under mild conditions that the Bayes factor gives the uniformly most powerful invariant test only if the prior for the coefficients being tested is an elliptical distribution with this scale matrix. The implications are discussed. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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