With flexible modeling software - such as the probabilistic programming language Stan - growing in popularity, quantities of interest (QOIs) calculated post-estimation are increasingly desired and customly implemented, both by statistical software developers and applied scientists. Examples of QOI include the marginal expectation of a multilevel model with a non-linear link function, or an ANOVA decomposition of a bivariate regression spline. For this, the QOI-Check is introduced, a systematic approach to ensure proper calibration and correct interpretation of QOIs. It contributes to Bayesian Workflow, and aims to improve the interpretability and trust in post-estimation conclusions based on QOIs. The QOI-Check builds upon Simulation Based Calibration (SBC), and the Holdout Predictive Check (HPC). SBC verifies computational reliability of Bayesian inference algorithms by consistency check of posterior with prior when the posterior is estimated on prior-predicted data, while HPC ensures robust inference by assessing consistency of model predictions with holdout data. SBC and HPC are combined in QOI-Checking for validating post-estimation QOI calculation and interpretation in the context of a (hypothetical) population definition underlying the QOI.

翻译：随着概率编程语言Stan等灵活建模软件的日益普及，由统计软件开发者和应用科学家在后验估计阶段计算并自定义实现的关注量（QOI）需求日益增长。QOI的示例包括具有非线性链接函数的多层模型的边际期望，或双变量回归样条的方差分析分解。为此，我们提出QOI-Check——一种系统化方法，用于确保QOI的正确校准与合理解释。该方法是对贝叶斯工作流的补充，旨在提升基于QOI的后验估计结论的可解释性与可信度。QOI-Check建立在仿真基准校准（SBC）与留出预测检验（HPC）的基础上：SBC通过在先验预测数据上估计后验分布时，检验后验与先验的一致性，以验证贝叶斯推断算法的计算可靠性；HPC则通过评估模型预测与留出数据的一致性来确保推断的稳健性。QOI-Check将SBC与HPC相结合，在QOI所基于的（假设性）总体定义的框架下，对后验估计中QOI的计算与解释进行验证。