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 pseudo likelihood of the ranks 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，边缘分布与Copula函数被分别设定。我们将二者视为模块化贝叶斯推断框架中的两个独立模块，并提出通过"切断反馈"进行修正贝叶斯推断。反馈切断限制了后验推断中可能被错误设定模块的影响。我们考虑两种切断类型：第一种限制错误设定的Copula对边缘分布推断的影响，这是经典边缘推断（IFM）估计量的贝叶斯类比；第二种通过使用秩的伪似然定义切断模型，限制错误设定的边缘分布对Copula参数推断的影响。我们证明若仅有一个模块被错误设定，则恰当的切断后验能为另一模块参数提供渐近准确的 uncertainty quantification。切断后验的计算具有挑战性，本文提出新的变分推断方法实现计算。通过模拟数据和宏观经济学预测中的多变量时间序列实际应用，验证了新方法的有效性。在后者案例中，与传统贝叶斯推断相比，从错误设定的边缘分布向1096维Copula的反馈切断显著改善了后验推断与预测精度。