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Hierarchical Shrinkage Priors for Regression Models

Griffin, Jim E., Brown, Philip J. (2017) Hierarchical Shrinkage Priors for Regression Models. Bayesian Analysis, 12 (1). pp. 135-159. ISSN 1936-0975. E-ISSN 1931-6690. (doi:10.1214/15-BA990) (KAR id:60987)

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http://dx.doi.org/10.1214/15-BA990

Abstract

In some linear models, such as those with interactions, it is natural to include the relationship between the regression coefficients in the analysis. In this paper, we consider how robust hierarchical continuous prior distributions can be used to express dependence between the size but not the sign of the regression coefficients. For example, to include ideas of heredity in the analysis of linear models with interactions. We develop a simple method for controlling the shrinkage of regression effects to zero at different levels of the hierarchy by considering the behaviour of the continuous prior at zero. Applications to linear models with interactions and generalized additive models are used as illustrations.

Item Type: Article
DOI/Identification number: 10.1214/15-BA990
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Jim Griffin
Date Deposited: 22 Mar 2017 11:50 UTC
Last Modified: 16 Feb 2021 13:44 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/60987 (The current URI for this page, for reference purposes)
Griffin, Jim E.: https://orcid.org/0000-0002-4828-7368
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