Approximate Cross-Validated Mean Estimates for Bayesian Hierarchical Regression Models
提出一种近似方法，避免对贝叶斯分层回归模型逐折重算，使大规模模型的交叉验证更可行，适用于留一法和留一簇法。
We introduce a novel procedure for obtaining cross-validated predictive estimates for Bayesian hierarchical regression models (BHRMs). BHRMs are popular for modeling complex dependence structures (e.g., Gaussian processes and Gaussian Markov random fields) 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 rerun computationally costly estimation methods for each cross-validation fold and makes CV more feasible for large BHRMs. We shift the CV problem from probability-based sampling to a familiar and straightforward optimization problem by conditioning on the variance-covariance parameters. Our approximation applies to leave-one-out CV and leave-one-cluster-out CV, the latter of which is more appropriate for models with complex dependencies. In many cases, this produces estimates equivalent to full CV. We provide theoretical results, demonstrate the efficacy of our method on publicly available data and in simulations, and compare the model performance with several competing methods for CV approximation. Code and other supplementary materials available online.