Approximate Cross-validated Mean Estimates for Bayesian Hierarchical Regression Models

TL;DR

This paper presents a new efficient method for cross-validating Bayesian hierarchical regression models, reducing computational costs and enabling practical predictive performance evaluation for complex models.

Contribution

The authors introduce a novel approximation technique that simplifies cross-validation for BHRMs, making it computationally feasible without sacrificing accuracy.

Findings

Method produces estimates often equivalent to full cross-validation.

Demonstrated effectiveness on real datasets and simulations.

Reduces computational time significantly for large models.

Abstract

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.