Parameter inference, i.e. inferring the posterior distribution of the parameters of a statistical model given some data, is a central problem to many scientific disciplines. Posterior inference with generative models is an alternative to methods such as Markov Chain Monte Carlo, both for likelihood-based and simulation-based inference. However, assessing the accuracy of posteriors encoded in generative models is not straightforward. In this paper, we introduce `distance to random point' (DRP) coverage testing as a method to estimate coverage probabilities of generative posterior estimators. Our method differs from previously-existing coverage-based methods, which require posterior evaluations. We prove that our approach is necessary and sufficient to show that a posterior estimator is optimal. We demonstrate the method on a variety of synthetic examples, and show that DRP can be used to test the results of posterior inference analyses in high-dimensional spaces. We also show that our method can detect non-optimal inferences in cases where existing methods fail.

翻译：参数推断，即根据给定数据推断统计模型参数的后验分布，是众多科学领域的核心问题。基于生成模型的后验推断，无论是用于基于似然的推断还是基于模拟的推断，都是马尔可夫链蒙特卡洛等方法的替代方案。然而，评估生成模型所编码的后验分布的准确性并非易事。本文提出了一种名为“到随机点的距离”（DRP）覆盖测试方法，用于估计生成后验估计器的覆盖概率。我们的方法不同于以往需要后验评估的基于覆盖的方法。我们证明，该方法对于证明后验估计器的最优性是必要且充分的。我们在多种合成示例上展示了该方法，并表明DRP可用于测试高维空间中后验推断分析的结果。此外，我们展示了该方法能够在现有方法失效的情况下检测出非最优的推断结果。