2013 Fiscal Year Final Research Report
Bayesian statistics based on shrinkage prior
| Project/Area Number |
23740067
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | The University of Tokyo |
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Principal Investigator |
MARUYAMA Yuzo 東京大学, 空間情報科学研究センター, 准教授 (30304728)
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| Project Period (FY) |
2011 – 2012
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| Keywords | ベイズ統計学 |
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| Research Abstract |
We study Bayesian variable selection in linear models with general spherically symmetric error distributions. We construct the posterior odds based on a separable prior function, which arises as a class of mixtures of Gaussians. The posterior odds for comparing among non-null models are shown to be independent of the underlying error distribution, provided that the distribution is spherically symmetric. Because of this invariance to spherically symmetric error distributions, we refer to our method as a robust Bayesian variable selection method. We demonstrate that our posterior odds have model selection consistency. Additionally we demonstrate that our class of prior function are the only ones within a large class of mixtures of Gaussians studied in the literature which are robust in our sense.
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