Hierarchical Shrinkage Priors for Regression Models

By Jim E. Griffin, Philip J. Brown. 2017

78 citations recorded by the source corpus.

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.

Subfields: Control and Systems Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/5b777f87b067c3e0bc0f33678a5298ba7bb897ae

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In Control and Systems Engineering

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Citations in the corpus

Adaptive Shrinkage in Bayesian Vector Autoregressive Models (2019, unknown): “To provide additional flexibility, we also extend the standard NG prior, similarly to Griffin and Brown (2017), by introducing additional global shrinkage parameters that exhibit symmetric shrinkage on certain regions of the parameter space.”
The Kernel Interaction Trick: Fast Bayesian Discovery of Pairwise Interactions in High Dimensions (2019, background): “Previous efforts [10, 15] have focused on developing hierarchical sparsity priors that promote strong hierarchy, analogous to the LASSO-based approaches [5, 18, 22, 35].”
Moving beyond noninformative priors: why and how to choose weakly informative priors in Bayesian analyses (2019, background): “The normal-gamma prior is the completely continuous version of the discrete spike-and-slab prior and, under certain α and β priors, similar in shape to the Laplace distribution (Griffin and Brown 2010, 2017).”