In Bayesian statistics, the marginal likelihood is used for model selection and averaging, yet it is often challenging to compute accurately for complex models. Approaches such as bridge sampling, while effective, may suffer from issues of high variability of the estimates. We present how to estimate Monte Carlo standard error (MCSE) for bridge sampling, and how to diagnose the reliability of MCSE estimates using Pareto-$\hat{k}$ and block reshuffling diagnostics without the need to repeatedly re-run full posterior inference. We demonstrate the behavior with increasingly more difficult simulated posteriors and many real posteriors from the posteriordb database.

翻译：在贝叶斯统计中，边缘似然常用于模型选择与平均，但对于复杂模型而言，其精确计算往往具有挑战性。桥式抽样等方法虽然有效，但可能面临估计值高变异性的问题。本文阐述了如何估计桥式抽样的蒙特卡洛标准误（MCSE），以及如何通过Pareto-$\hat{k}$诊断与区块重排诊断来评估MCSE估计的可靠性，而无需重复运行完整的后验推断。我们通过难度递增的模拟后验分布及来自posteriordb数据库的大量真实后验分布案例，展示了该方法的实际表现。