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Leave-one-out cross-validation (LOO-CV) is a popular method for estimatingout-of-sample predictive accuracy. However, computing LOO-CV criteria can becomputationally expensive due to the need to fit the model multiple times. Inthe Bayesian context, importance sampling provides a possible solution butclassical approaches can easily produce estimators whose asymptotic variance isinfinite, making them potentially unreliable. Here we propose and analyze anovel mixture estimator to compute Bayesian LOO-CV criteria. Our method retainsthe simplicity and computational convenience of classical approaches, whileguaranteeing finite asymptotic variance of the resulting estimators. Boththeoretical and numerical results are provided to illustrate the improvedrobustness and efficiency. The computational benefits are particularlysignificant in high-dimensional problems, allowing to perform Bayesian LOO-CVfor a broader range of models, and datasets with highly influentialobservations. The proposed methodology is easily implementable in standardprobabilistic programming software and has a computational cost roughlyequivalent to fitting the original model once.

Robust leave-one-out cross-validation for high-dimensional Bayesian models