Approximate Cross-validated Mean Estimates for Bayesian Hierarchical Regression Models
This method addresses the computational bottleneck of cross-validation for researchers and practitioners using Bayesian hierarchical regression models, making model evaluation more accessible.
This paper introduces a new procedure for obtaining cross-validated predictive estimates for Bayesian hierarchical regression models (BHRMs). The method avoids re-running computationally expensive estimation for each CV fold, making CV more feasible for large BHRMs by transforming the problem into an optimization task.
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.