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March 2017 Hierarchical Shrinkage Priors for Regression Models
Jim Griffin, Phil Brown
Bayesian Anal. 12(1): 135-159 (March 2017). DOI: 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.

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Jim Griffin. Phil Brown. "Hierarchical Shrinkage Priors for Regression Models." Bayesian Anal. 12 (1) 135 - 159, March 2017. https://doi.org/10.1214/15-BA990

Information

Published: March 2017
First available in Project Euclid: 19 January 2016

zbMATH: 1384.62225
MathSciNet: MR3597570
Digital Object Identifier: 10.1214/15-BA990

Keywords: Bayesian regularization , generalized additive models , generalized beta mixture prior , interactions , normal-gamma prior , normal-gamma-gamma prior , strong and weak heredity , structured priors

Rights: Copyright © 2017 International Society for Bayesian Analysis

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Vol.12 • No. 1 • March 2017
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