Department of Statistics, Harvard University, Cambridge, MA 02138.
Spotify, New York, NY 10011.
Proc Natl Acad Sci U S A. 2020 Jun 2;117(22):12004-12010. doi: 10.1073/pnas.1920913117. Epub 2020 May 15.
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.
设计催化先验分布是为了通过将高维“工作模型”向“简化模型”收缩来稳定它。收缩是通过用从更简单模型下的预测分布生成的少量“合成数据”来补充观测数据来实现的。我们将此框架应用于广义线性模型，其中我们提出了各种策略来指定控制收缩程度的调整参数，并研究了由此产生的理论性质。在模拟中，使用这种催化先验的后验估计优于工作模型的最大似然估计，并且在点估计的频率预测准确性和区间估计的覆盖准确性方面，通常与现有的竞争方法相当或优于现有的竞争方法。催化先验具有简单的解释，并且易于制定。
