In copula models the marginal distributions and copula function are specified separately. We treat these as two modules in a modular Bayesian inference framework, and propose conducting modified Bayesian inference by ``cutting feedback''. Cutting feedback limits the influence of potentially misspecified modules in posterior inference. We consider two types of cuts. The first limits the influence of a misspecified copula on inference for the marginals, which is a Bayesian analogue of the popular Inference for Margins (IFM) estimator. The second limits the influence of misspecified marginals on inference for the copula parameters by using a rank likelihood to define the cut model. We establish that if only one of the modules is misspecified, then the appropriate cut posterior gives accurate uncertainty quantification asymptotically for the parameters in the other module. Computation of the cut posteriors is difficult, and new variational inference methods to do so are proposed. The efficacy of the new methodology is demonstrated using both simulated data and a substantive multivariate time series application from macroeconomic forecasting. In the latter, cutting feedback from misspecified marginals to a 1096 dimension copula improves posterior inference and predictive accuracy greatly, compared to conventional Bayesian inference.

翻译：在Copula模型中，边际分布与Copula函数被分别设定。我们将两者视为模块化贝叶斯推断框架中的两个模块，并提出通过“反馈截断”实施修正贝叶斯推断。反馈截断限制了潜在误设定模块在后验推断中的影响。本文考虑两类截断：第一类限制误设定的Copula对边际分布推断的影响，这是流行的“边际推断法”（IFM）估计量的贝叶斯对应；第二类通过使用秩似然定义截断模型，限制误设定的边际分布对Copula参数推断的影响。我们证明：若仅有一个模块被误设定，则适当的截断后验能够为另一模块的参数提供渐近精确的不确定性量化。截断后验的计算存在困难，为此本文提出了新的变分推断方法。通过模拟数据及宏观经济预测中一个实质性的多元时间序列应用，验证了新方法的有效性。在后一应用中，从误设定的边际分布到1096维Copula的反馈截断，相比传统贝叶斯推断，显著提升了后验推断与预测精度。