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Catalytic prior distributions with application to generalized linear models

Huang, D
; 
Stein, N
; 
Rubin, DB
; 
Kou, SC
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Journal Article
Date
2020-06-02
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Bayesian priors
 synthetic data
 stable estimation
 predictive distribution
 regularization
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http://hdl.handle.net/20.500.12613/4250
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Catalytic prior distributions with application to generalized linear models.pdf
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DOI
10.1073/pnas.1920913117
Abstract
© 2020 National Academy of Sciences. All rights reserved. A catalytic prior distribution is designed to stabilize a high-dimensional “working model” by shrinking it toward a “simplified model.” The shrinkage is achieved by supplementing the observed data with a small amount of “synthetic data” generated from a predictive distribution under the simpler model. We apply this framework to generalized linear models, where we propose various strategies for the specification of a tuning parameter governing the degree of shrinkage and study resultant theoretical properties. In simulations, the resulting posterior estimation using such a catalytic prior outperforms maximum likelihood estimation from the working model and is generally comparable with or superior to existing competitive methods in terms of frequentist prediction accuracy of point estimation and coverage accuracy of interval estimation. The catalytic priors have simple interpretations and are easy to formulate.
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Proceedings of the National Academy of Sciences
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Proceedings of the National Academy of Sciences of the United States of America
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