Bayesian Working Group: Jarad Niemi, Catalytic Priors

Bayesian Working Group: Jarad Niemi, Catalytic Priors

Feb 3, 2023 - 12:00 PM
to Feb 3, 2023 - 1:00 PM

Jarad Niemi will lead a discussion about catalytic priors as described in the manuscript "Catalytic prior distributions with application togeneralized linear models." The abstract for this manuscript is below:

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.