Approximate Cross-validated Mean Estimates for Bayesian Hierarchical Regression Models
CoRR(2020)
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.
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