Catalytic prior distributions with application to generalized linear models
Catalytic prior distributions with application to generalized linear models
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DOI：
10.1073/pnas.1920913117
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发表时间：
2020-06-02
影响因子：
11.1
通讯作者：
Kou, S. C.
中科院分区：
文献类型：
--
作者：
Huang, Dongming;Stein, Nathan;Kou, S. C.
催化先验分布被设计成通过将高维“工作模型”向“简化模型”收缩来稳定它。“收缩是通过用少量的“合成数据”补充观测数据来实现的，这些数据是在更简单的模型下从预测分布中生成的。我们将此框架应用于广义线性模型，在那里我们提出了各种策略的规格调整参数的收缩程度和研究所得的理论性质。在模拟中，所得到的后验估计使用这样的催化先验优于最大似然估计从工作模型，一般是可比的或上级现有的竞争方法的频率预测精度的点估计和区间估计的覆盖精度。催化先验有简单的解释，很容易制定。
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.