Abstract Gaussian graphical models (GGM; partial correlation networks) have become increasingly popular in the social and behavioral sciences for studying conditional (in)dependencies between variables. In this work, we introduce exploratory and confirmatory Bayesian tests for partial correlations. For the former, we first extend the customary GGM formulation that focuses on conditional dependence to also consider the null hypothesis of conditional independence for each partial correlation. Here a novel testing strategy is introduced that can provide evidence for a null, negative, or positive effect. We then introduce a test for hypotheses with order constraints on partial correlations. This allows for testing theoretical and clinical expectations in GGMs. The novel matrix- F prior distribution is described that provides increased flexibility in specification compared to the Wishart prior. The methods are applied to PTSD symptoms. In several applications, we demonstrate how the exploratory and confirmatory approaches can work in tandem: hypotheses are formulated from an initial analysis and then tested in an independent dataset. The methodology is implemented in the R package BGGM .

中文翻译：

---

高斯图形模型的贝叶斯假设检验：条件独立性和顺序约束

摘要 高斯图模型（GGM；部分相关网络）在社会和行为科学中越来越流行，用于研究变量之间的条件（不）依赖性。在这项工作中，我们引入了偏相关的探索性和验证性贝叶斯检验。对于前者，我们首先扩展关注条件依赖的惯用 GGM 公式，以考虑每个偏相关的条件独立性的原假设。这里引入了一种新颖的测试策略，可以为无效、负面或正面影响提供证据。然后，我们引入了对偏相关性具有顺序约束的假设的检验。这允许在 GGM 中测试理论和临床预期。描述了新的矩阵 F 先验分布，与 Wishart 先验相比，它在规范方面提供了更大的灵活性。这些方法适用于 PTSD 症状。在几个应用程序中，我们展示了探索性和验证性方法如何协同工作：假设是从初始分析中制定的，然后在独立的数据集中进行测试。该方法在 R 包 BGGM 中实现。