Gaussian graphical models provide a powerful framework for studying conditional dependencies in multivariate data, with widespread applications spanning biomedical, environmental sciences, and other data-rich scientific domains. While the Graphical Horseshoe (GHS) method has emerged as a state-of-the-art Bayesian method for sparse precision matrix estimation, existing approaches assume fully observed data and thus fail in the presence of censoring or missingness, which are pervasive in real-world studies. In this paper, we develop the Censored Graphical Horseshoe (CGHS), a novel Bayesian framework that extends the GHS to censored and arbitrarily missing Gaussian data. By introducing a latent-variable representation, CGHS accommodates incomplete observations while retaining the adaptive global-local shrinkage properties of the Horseshoe prior. We derive efficient Gibbs samplers for posterior computation and establish new theoretical results on posterior behavior under censoring and missingness, filling a gap not addressed by frequentist Lasso-based methods. Through extensive simulations, we demonstrate that CGHS consistently improves estimation accuracy compared to penalized likelihood approaches. Our methods are implemented in the package GHScenmis available on Github: https://github.com/tienmt/ghscenmis .

翻译：高斯图模型为研究多元数据中的条件依赖关系提供了强大框架，其应用广泛涵盖生物医学、环境科学及其他数据密集型科学领域。尽管图马靴方法已成为稀疏精度矩阵估计的前沿贝氏方法，但现有方法均假设数据完全观测，因此在存在删失或缺失时失效——而这在实际研究中普遍存在。本文提出删失图马靴这一新型贝氏框架，将图马靴扩展至含删失与任意缺失的高斯数据。通过引入潜变量表征，删失图马靴在保留马靴先验自适应全局-局部收缩特性的同时，兼容不完整观测。我们推导了高效吉布斯采样器进行后验计算，并建立了删失与缺失条件下后验行为的新理论结果，填补了基于频率学派Lasso方法未涉及的研究空白。通过大量模拟实验，我们证明相较于惩罚似然方法，删失图马靴能持续提升估计精度。本方法已实现于GHScenmis软件包，可通过Github获取：https://github.com/tienmt/ghscenmis 。