标题： 关于任意稀疏精度矩阵的新分层分布 显示英文标题

标题： A new hierarchical distribution on arbitrary sparse precision matrices

摘要： 我们提出了一种定义稀疏对称正定矩阵空间上分布的一般策略。 我们的方法利用了精度矩阵的Cholesky分解，通过对元素施加约束来实现稀疏性，同时保持它们的独立性并避免归一化常数的数值评估。 特别是，我们将S-Bartlett作为修改后的Bartlett分解开发出来，并将其作为标准Wishart分布的一个特例恢复。 通过引入Spike-and-Slab先验来建模图的稀疏性，我们的方法通过基于Dual Averaging Hamiltonian Monte Carlo更新的定制MCMC过程促进了贝叶斯估计。 此框架自然扩展到广义线性模型设置，通过潜在高斯变量实现了非高斯结果的应用。 我们在模拟和真实数据上测试并比较了提出的S-Bartlett先验与G-Wishart。 结果表明，S-Bartlett先验为估计稀疏精度矩阵提供了灵活的替代方案，在不同领域具有潜在应用。 显示英文摘要

摘要： We introduce a general strategy for defining distributions over the space of sparse symmetric positive definite matrices. Our method utilizes the Cholesky factorization of the precision matrix, imposing sparsity through constraints on its elements while preserving their independence and avoiding the numerical evaluation of normalization constants. In particular, we develop the S-Bartlett as a modified Bartlett decomposition, recovering the standard Wishart as a particular case. By incorporating a Spike-and-Slab prior to model graph sparsity, our approach facilitates Bayesian estimation through a tailored MCMC routine based on a Dual Averaging Hamiltonian Monte Carlo update. This framework extends naturally to the Generalized Linear Model setting, enabling applications to non-Gaussian outcomes via latent Gaussian variables. We test and compare the proposed S-Bartelett prior with the G-Wishart both on simulated and real data. Results highlight that the S-Bartlett prior offers a flexible alternative for estimating sparse precision matrices, with potential applications across diverse fields.