Leave-one-out cross-validation (LOO-CV) is a popular method for estimating out-of-sample predictive accuracy. However, computing LOO-CV criteria can be computationally expensive due to the need to fit the model multiple times. In the Bayesian context, importance sampling provides a possible solution but classical approaches can easily produce estimators whose variance is infinite, making them potentially unreliable. Here we propose and analyze a novel mixture estimator to compute Bayesian LOO-CV criteria. Our method retains the simplicity and computational convenience of classical approaches, while guaranteeing finite variance of the resulting estimators. Both theoretical and numerical results are provided to illustrate the improved robustness and efficiency. The computational benefits are particularly significant in high-dimensional problems, allowing to perform Bayesian LOO-CV for a broader range of models. The proposed methodology is easily implementable in standard probabilistic programming software and has a computational cost roughly equivalent to fitting the original model once.

翻译：在巴伊西亚,重要抽样提供了可能的解决办法,但典型的方法很容易得出差异无限的估测器。我们在这里提议并分析一种新颖的混合物估计器,用于计算Bayesian LOO-CV的标准。我们的方法保留了古典方法的简单性和计算便利,同时保证了由此产生的估计器的有限差异。提供了理论和数字结果,以说明改进后的稳健性和效率。计算效益在高维度问题上特别显著,使得能够执行Bayesian LOO-CV的模型范围更广。拟议的方法很容易在标准概率性编程软件中实施,计算成本大致相当于一次原始模型。