论文标题
贝叶斯分层回归模型的近似交叉验证平均估计值
Approximate Cross-validated Mean Estimates for Bayesian Hierarchical Regression Models
论文作者
论文摘要
我们引入了一种新的程序，用于获得贝叶斯分层回归模型（BHRMS）的交叉验证预测估计。贝叶斯分层模型因其对复杂依赖性结构建模并提供概率不确定性估计的能力而受欢迎，但运行在计算上可能很昂贵。因此，交叉验证（CV）不是评估BHRM的预测性能的普遍做法。我们的方法规定了每个交叉验证折叠的重新运行计算量估计方法的需求，并使CV对于大BHRM的可行性更为可行。通过对方差 - 协方差参数进行调节，我们将CV问题从基于概率的采样转移到简单且熟悉的优化问题。在许多情况下，这会产生相当于完整简历的估计值。我们提供理论结果，并在公开数据和模拟中证明其功效。
We introduce a novel procedure for obtaining cross-validated predictive estimates for Bayesian hierarchical regression models (BHRMs). Bayesian hierarchical models are popular for their ability to model complex dependence structures and provide probabilistic uncertainty estimates, but can be computationally expensive to run. Cross-validation (CV) is therefore not a common practice to evaluate the predictive performance of BHRMs. Our method circumvents the need to re-run computationally costly estimation methods for each cross-validation fold and makes CV more feasible for large BHRMs. By conditioning on the variance-covariance parameters, we shift the CV problem from probability-based sampling to a simple and familiar optimization problem. In many cases, this produces estimates which are equivalent to full CV. We provide theoretical results and demonstrate its efficacy on publicly available data and in simulations.
