单因子图模型的贝叶斯推断
Bayesian Inference for Single-factor Graphical Models
AI总结：
本文提出单因子图模型的贝叶斯推断方法，通过MCMC算法处理相关残差，并扩展至分类变量及多数据集，以捕捉时空关联和条件依赖结构。
摘要：
我们引入了高效的MCMC算法，用于对具有相关残差的单因子模型进行贝叶斯推断，其中残差的分布为高斯图模型。我们将这类模型称为单因子图模型。我们将单因子图模型扩展到包含二元和有序分类变量的数据集，以及空间或时间上相关的多个数据集的建模。我们的模型能够通过潜在因子捕捉跨时间和空间的多变量关联，并通过高斯图模型捕捉每个空间位置或时间点上的残差条件依赖结构。我们在模拟和真实世界示例中展示了单因子图模型的应用。
英文摘要：
We introduce efficient MCMC algorithms for Bayesian inference for single-factor models with correlated residuals where the residuals' distribution is a Gaussian graphical model. We call this family of models single-factor graphical models. We extend single-factor graphical models to datasets that also involve binary and ordinal categorical variables and to the modeling of multiple datasets that are spatially or temporally related. Our models are able to capture multivariate associations through latent factors across time and space, as well as residual conditional dependence structures at each spatial location or time point through Gaussian graphical models. We illustrate the application of single-factor graphical models in simulated and real-world examples.
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