Modern datasets commonly feature both substantial missingness and many variables of mixed data types, which present significant challenges for estimation and inference. Complete case analysis, which proceeds using only the observations with fully-observed variables, is often severely biased, while model-based imputation of missing values is limited by the ability of the model to capture complex dependencies among (possibly many) variables of mixed data types. To address these challenges, we develop a novel Bayesian mixture copula for joint and nonparametric modeling of multivariate count, continuous, ordinal, and unordered categorical variables, and deploy this model for inference, prediction, and imputation of missing data. Most uniquely, we introduce a new and computationally efficient strategy for marginal distribution estimation that eliminates the need to specify any marginal models yet delivers posterior consistency for each marginal distribution and the copula parameters under missingness-at-random. Extensive simulation studies demonstrate exceptional modeling and imputation capabilities relative to competing methods, especially with mixed data types, complex missingness mechanisms, and nonlinear dependencies. We conclude with a data analysis that highlights how improper treatment of missing data can distort a statistical analysis, and how the proposed approach offers a resolution.

翻译：现代数据集通常同时包含大量缺失值和多种混合类型变量，这给估计和推断带来了显著挑战。仅使用完全观测变量的完整案例分析往往存在严重偏倚，而基于模型的缺失值插补能力受限于模型捕捉（可能大量的）混合类型变量间复杂依赖关系的能力。为应对这些挑战，我们提出了一种新颖的贝叶斯混合Copula模型，用于对多元计数、连续、有序和无序分类变量进行联合非参数建模，并将其应用于缺失数据的推断、预测和插补。最具创新性的是，我们引入了一种计算高效的边际分布估计策略，无需指定任何边际模型，即可在随机缺失假设下保证各边际分布和Copula参数的后验相合性。大量模拟研究表明，与竞争方法相比，本方法在建模和插补能力上表现卓越，尤其适用于混合数据类型、复杂缺失机制和非线性依赖场景。最后，通过一项数据分析，我们展示了不当处理缺失数据如何扭曲统计分析，以及所提出的方法如何提供解决方案。