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A0273
Title: Catalytic priors: Using synthetic data to specify prior distributions in Bayesian analysis Authors:  Dongming Huang - National University of Singapore (China) [presenting]
Feicheng Wang - Harvard University (United States)
Donald Rubin - Harvard University (United States)
Samuel Kou - Harvard University (United States)
Abstract: Catalytic prior distributions provide general, easy-to-use, and interpretable specifications of prior distributions for Bayesian analysis. They are particularly beneficial when observed data are inadequate to well-estimate a complex target model. A prior catalytic distribution stabilizes 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. This framework is applied to generalized linear models, where various strategies are proposed for specifying a tuning parameter governing the degree of shrinkage and resultant properties are studied. The catalytic priors have simple interpretations and are easy to formulate. In our numerical experiments and a real-world study, the performance of the inference based on the catalytic prior is superior to or comparable to that of other commonly used prior distributions.