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.

翻译：我们采用了一种新颖的程序来获得对贝叶斯人级回归模型的交叉有效预测估计。贝叶斯人的等级模型因其能够模拟复杂的依赖结构并提供概率性不确定性估计,而很受欢迎,但可以计算出昂贵的运行费用。因此,交叉验证(CV)并不是评价贝叶斯人级回归模型预测性能的常见做法。我们的方法避免了对每个交叉验证折叠进行计算成本高昂的估计方法的重新运行的必要性,并使大型BHRM更适合CV。我们根据差异变量参数调整了CV问题,从基于概率的抽样转变为简单和熟悉的优化问题。在许多情况下,这产生了相当于完整的CV的估计数。我们提供了理论结果,并用公开的数据和模拟来展示其有效性。