Parametric Bayesian modeling offers a powerful and flexible toolbox for scientific data analysis. Yet the model, however detailed, may still be wrong, and this can make inferences untrustworthy. In this paper we study nonparametrically perturbed parametric (NPP) Bayesian models, in which a parametric Bayesian model is relaxed via a distortion of its likelihood. We analyze the properties of NPP models when the target of inference is the true data distribution or some functional of it, such as in causal inference. We show that NPP models can offer the robustness of nonparametric models while retaining the data efficiency of parametric models, achieving fast convergence when the parametric model is close to true. To efficiently analyze data with an NPP model, we develop a generalized Bayes procedure to approximate its posterior. We demonstrate our method by estimating causal effects of gene expression from single cell RNA sequencing data. NPP modeling offers an efficient approach to robust Bayesian inference and can be used to robustify any parametric Bayesian model.

翻译：参数贝叶斯建模为科学数据分析提供了一个强大而灵活的工具箱。然而，无论模型多么精细，仍可能存在错误，这可能导致推断结果不可信。本文研究非参数扰动参数（NPP）贝叶斯模型，其中通过扭曲似然函数来松弛参数贝叶斯模型。我们分析了当推断目标是真实数据分布或其某个泛函（例如在因果推断中）时，NPP模型的性质。研究表明，NPP模型能够提供非参数模型的鲁棒性，同时保留参数模型的数据效率，当参数模型接近真实情况时实现快速收敛。为有效利用NPP模型分析数据，我们开发了一种广义贝叶斯程序来近似其后验分布。我们通过估计单细胞RNA测序数据中基因表达的因果效应来验证所提方法。NPP建模为鲁棒贝叶斯推断提供了一种高效途径，可用于强化任何参数贝叶斯模型。