通过无穷小杰克逊法计算贝叶斯后验函数的稳健标准误差
Robust Standard Errors for Bayesian Posterior Functionals via the Infinitesimal Jackknife
AI总结：
本文提出一种通过单次MCMC运行计算后验函数稳健标准误差的方法，适用于多种统计分析，相比传统方法更高效且抗模型误设。
摘要：
社会科学中的定量研究严重依赖非线性后验函数，如间接效应、标准化系数、效应量、组内相关性和多层方差解释措施。后验标准差（PostSD）是这些量的默认不确定性总结，但假设模型正确指定。当工作模型错误时，如行为数据存在厚尾和异方差，PostSD会严重低估频繁标准误差。非参数自助法提供鲁棒性但需要重复MCMC重拟合，而delta方法需要为每个新功能导出单独的分析梯度。无穷小杰克逊标准误差（Giordano & Broderick, 2023）避免了这两种限制：它通过从单次MCMC运行计算的影响力函数近似自助法方差，适用于任何后验函数且无需修改，也不需要分析导数。我们讨论了在观测水平和聚类水平使用IJSE方法，并通过四个模拟研究评估，涵盖中介分析、方差分析和多层建模的六个功能。在模型误设下，PostSD在所有设置中都严重低估了真实标准误差，而IJSE在计算成本低的情况下接近自助法。在正确指定模型下，三种方法一致，证实IJSE在模型正确时无失真。这些结果表明IJSE是一种实用的、通用的工具，用于在社会科学中的贝叶斯工作流程中进行稳健的不确定性量化。
英文摘要：
Quantitative research in the social and behavioral sciences relies heavily on nonlinear posterior functionals such as indirect effects, standardized coefficients, effect sizes, intraclass correlations, and multilevel variance-explained measures. The posterior standard deviation (PostSD) is the default uncertainty summary for these quantities, yet it presupposes a correctly specified model. When the working model is wrong, as is common with behavioral data that exhibit heavy tails and heteroskedasticity, PostSD can severely underestimate the frequentist standard error. The nonparametric bootstrap offers robustness but requires repeated MCMC refits, while the delta method demands a separate analytic gradient derivation for every new functional. The infinitesimal jackknife standard error (Giordano & Broderick, 2023) sidesteps both limitations: it approximates the bootstrap variance through influence functions computed from a single MCMC run, applies to any posterior functional without modification, and requires no analytic derivatives. We discuss the use the IJSE methodology at both the observation level and the cluster level and evaluate it through four simulation studies covering six functionals from mediation analysis, ANOVA, and multilevel modeling, which are commonly used in the social and behavioral sciences. Under misspecification, PostSD substantially underestimated the true standard error across all settings, whereas IJSE closely tracked the bootstrap at a fraction of the computational cost. Under correct specification all three methods agreed, confirming that IJSE introduces no distortion when the model is right. These results show IJSE as a practical, general-purpose tool for robust uncertainty quantification in Bayesian workflows throughout the social and behavioral sciences
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