截断图形马蹄：具有截断和缺失数据的贝叶斯稀疏精度矩阵估计
Censored Graphical Horseshoe: Bayesian sparse precision matrix estimation with censored and missing data
AI总结：
本文提出CGHS方法，用于处理截断和缺失数据的贝叶斯稀疏精度矩阵估计，通过引入潜在变量和自适应收缩先验，提高估计精度。
摘要：
高斯图形模型为研究多元数据中的条件依赖性提供了强大的框架，其应用范围广泛，涵盖了生物医学、环境科学和其他数据丰富的科学领域。尽管图形马蹄（GHS）方法已成为稀疏精度矩阵估计的最先进的贝叶斯方法，但现有方法假设数据完全观测，因此在存在截断或缺失时会失效，这在现实研究中普遍存在。在本文中，我们开发了截断图形马蹄（CGHS），一种新的贝叶斯框架，将其扩展到截断和任意缺失的高斯数据。通过引入潜在变量表示，CGHS在保留马蹄先验的自适应全局-局部收缩特性的同时，能够处理不完整观测。我们推导了后验计算的高效吉布斯采样器，并在截断和缺失情况下建立了新的理论结果，填补了频率学Lasso方法未解决的空白。通过广泛的模拟，我们证明CGHS在与惩罚似然方法相比时，能够一致地提高估计精度。我们的方法在GitHub上实现为GHScenmis包：https://github.com/tienmt/ghscenmis。
英文摘要：
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 .
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
