标题： 基于贝叶斯自助法的高缺失率混合数据高斯Copula模型 显示英文标题

标题： Bayesian Bootstrap based Gaussian Copula Model for Mixed Data with High Missing Rates

摘要： 缺失数据是医学、社会科学和自然科学等多个领域中的常见问题，并对准确的统计分析构成了重大挑战。 尽管已经提出了许多插补方法来解决这个问题，但其中许多方法未能充分捕捉变量之间的复杂依赖结构。 为了克服这一限制，引入了基于高斯copula框架的模型。 然而，大多数现有的基于copula的方法没有考虑边缘分布中的不确定性，这可能导致边缘估计偏差和性能下降，尤其是在高缺失率的情况下。 在本研究中，我们提出了一种基于贝叶斯自助法的高斯Copula模型（BBGC），该模型明确地将每个变量的边缘分布中的不确定性纳入考虑。 所提出的BBGC结合了高斯copula的灵活依赖建模能力，以及通过贝叶斯自助法对边缘累积分布函数（CDF）进行贝叶斯不确定性量化。 此外，通过引入有序变量建模方法，该模型被扩展以处理混合数据类型。 通过模拟研究和对来自UCI存储库的真实数据集的实验，我们证明所提出的BBGC在各种缺失率和机制（MCAR，MAR）下均优于现有的插补方法。 此外，与传统插补方法相比，所提出的模型在真实半导体制造过程数据上的表现更为优越。 显示英文摘要

摘要： Missing data is a common issue in various fields such as medicine, social sciences, and natural sciences, and it poses significant challenges for accurate statistical analysis. Although numerous imputation methods have been proposed to address this issue, many of them fail to adequately capture the complex dependency structure among variables. To overcome this limitation, models based on the Gaussian copula framework have been introduced. However, most existing copula-based approaches do not account for the uncertainty in the marginal distributions, which can lead to biased marginal estimates and degraded performance, especially under high missingness rates. In this study, we propose a Bayesian bootstrap-based Gaussian Copula model (BBGC) that explicitly incorporates uncertainty in the marginal distributions of each variable. The proposed BBGC combines the flexible dependency modeling capability of the Gaussian copula with the Bayesian uncertainty quantification of marginal cumulative distribution functions (CDFs) via the Bayesian bootstrap. Furthermore, it is extended to handle mixed data types by incorporating methods for ordinal variable modeling. Through simulation studies and experiments on real-world datasets from the UCI repository, we demonstrate that the proposed BBGC outperforms existing imputation methods across various missing rates and mechanisms (MCAR, MAR). Additionally, the proposed model shows superior performance on real semiconductor manufacturing process data compared to conventional imputation approaches.