Griffin, J;
Brown, P;
(2017)
Hierarchical shrinkage priors for regression models.
Bayesian Analysis
, 12
(1)
pp. 135-159.
10.1214/15-BA990.
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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.
| Type: | Article |
|---|---|
| Title: | Hierarchical shrinkage priors for regression models |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1214/15-BA990 |
| Publisher version: | https://doi.org/10.1214/15-BA990 |
| Language: | English |
| Additional information: | This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Bayesian regularization, interactions, structured priors, strong and weak heredity, generalized additive models, normal-gamma prior, normal-gamma-gamma prior, generalized beta mixture prior |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10068477 |
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