Leave-one-out cross-validation for non-factorizable normal models
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Cross-validation can be used to measure a model's predictive accuracy for instance for the purpose of model comparison or selection. As exact cross-validation is often practically infeasible for Bayesian models because it requires too much time, approximate cross-validation methods have been developed; most notably methods for leave-one-out cross-validation (LOO-CV). However, standard LOO-CV requires the likelihood to be factorizable, that is the observations have to be conditionally independent given the model parameters. Unfortunately, some important statistical models most notably in the context of temporal and spatial statistics are non-factorizable, but LOO-CV may still be an important measure for these models. For this reason, we derive how to compute and validate exact and approximate LOO-CV for non-factorizable models that follow a multivariate normal likelihood.
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