Complex statistical models are often built by combining multiple submodels, called modules. Here we consider modular inference where the modules contain both parametric and nonparametric components. In such cases, standard Bayesian inference can be highly sensitive to misspecification in any module, and influential prior specifications for the nonparametric components can compromise inference for the parametric components, and vice versa. We propose a novel "optimization-centric" approach to cutting feedback for semiparametric modular inference, which can address misspecification and prior-data conflicts. The proposed cut posteriors are defined via a variational optimization problem like other generalized posteriors, but regularization is based on Rényi divergence, instead of Kullback-Leibler divergence (KLD). We show empirically that defining the cut posterior using Rényi divergence delivers more robust inference than KLD, and Rényi divergence reduces the tendency to underestimate uncertainty when the variational approximations impose strong parametric or independence assumptions. Novel posterior concentration results that accommodate the Rényi divergence and allow for semiparametric components are derived, extending existing results for cut posteriors that only apply to KLD and parametric models. These new methods are demonstrated in a benchmark example and two real examples: Gaussian process adjustments for confounding in causal inference and misspecified copula models with nonparametric marginals.

翻译：复杂统计模型通常由多个子模型（称为模块）组合而成。本文考虑同时包含参数与非参数成分的模块化推断。在此类情形下，标准贝叶斯推断对任意模块的设定错误高度敏感，且非参数成分的先验设定会影响参数成分的推断，反之亦然。我们提出一种新颖的"优化导向"半参数模块化推断反馈切断方法，可有效处理设定错误与先验-数据冲突问题。所提出的切断后验分布与其他广义后验分布类似，通过变分优化问题定义，但其正则化基于Rényi散度而非KL散度。实验表明，基于Rényi散度的切断后验分布比KL散度能提供更稳健的推断，且当变分近似施加强参数性或独立性假设时，Rényi散度可降低不确定性低估的倾向。我们推导了新的后验集中性结果，该结果兼容Rényi散度并允许半参数成分存在，扩展了仅适用于KL散度与参数模型的现有切断后验结果。这些新方法通过一个基准示例及两个实际案例进行验证：因果推断中利用高斯过程调整混淆效应，以及具有非参数边际分布的错误设定copula模型。