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.

交叉验证可用于测量模型的预测准确性，以进行模型比较，平均或选择。标准的留一法交叉验证（LOO-CV）要求可以将观察模型分解为简单的术语，但是时空统计中的许多重要模型都没有这种性质，或者在被强制引入时不能有效或不稳定因式分解形式。我们推导了如何针对结果值具有多元正态或Student- \（t \）分布的任何贝叶斯非因式模型有效地计算和验证精确和近似LOO-CV 。我们演示了使用滞后同时自回归（SAR）模型作为案例研究的方法。