Efficient leave-one-out cross-validation for Bayesian non-factorized normal and Student-t models

TL;DR

This paper introduces an efficient method for leave-one-out cross-validation applicable to Bayesian non-factorized models with multivariate normal or Student-t distributions, enhancing model validation in complex spatial and temporal models.

Contribution

It derives a novel approach to compute exact and approximate LOO-CV efficiently for non-factorized Bayesian models, extending validation capabilities beyond traditional factorized models.

Findings

Method works for models with multivariate normal or Student-t distributions.

Demonstrated on lagged SAR models as a case study.

Improves computational efficiency and stability of LOO-CV.

Abstract

Cross-validation can be used to measure a model's predictive accuracy for the purpose of model comparison, averaging, or selection. Standard leave-one-out cross-validation (LOO-CV) requires that the observation model can be factorized into simple terms, but a lot of important models in temporal and spatial statistics do not have this property or are inefficient or unstable when forced into a factorized form. We derive how to efficiently compute and validate both exact and approximate LOO-CV for any Bayesian non-factorized model with a multivariate normal or Student-t distribution on the outcome values. We demonstrate the method using lagged simultaneously autoregressive (SAR) models as a case study.