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

arXiv: https://arxiv.org/abs/1810.10559 · HTML: https://mlsanity.com/paper/1810.10559/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Oct 2018.

## Built on by (most cited first, 3 of 3)

- [JANA: Jointly Amortized Neural Approximation of Complex Bayesian Models](https://mlsanity.com/paper/2302.09125/) (2023)
- [Fast and Scalable Spike and Slab Variable Selection in High-Dimensional Gaussian Processes](https://mlsanity.com/paper/2111.04558/) (2021)
- [Amortized Bayesian Mixture Models](https://mlsanity.com/paper/2501.10229/) (2025)

## Abstract (arXiv)

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.