Neighborhood selection is a widely used method used for estimating the support set of sparse precision matrices, which helps determine the conditional dependence structure in undirected graphical models. However, reporting only point estimates for the estimated graph can result in poor replicability without accompanying uncertainty estimates. In fields such as psychology, where the lack of replicability is a major concern, there is a growing need for methods that can address this issue. In this paper, we focus on the Gaussian graphical model. We introduce a selective inference method to attach uncertainty estimates to the selected (nonzero) entries of the precision matrix and decide which of the estimated edges must be included in the graph. Our method provides an exact adjustment for the selection of edges, which when multiplied with the Wishart density of the random matrix, results in valid selective inferences. Through the use of externally added randomization variables, our adjustment is easy to compute, requiring us to calculate the probability of a selection event, that is equivalent to a few sign constraints and that decouples across the nodewise regressions. Through simulations and an application to a mobile health trial designed to study mental health, we demonstrate that our selective inference method results in higher power and improved estimation accuracy.

翻译：邻域选择是一种广泛用于估计稀疏精度矩阵支撑集的方法，该方法有助于确定无向图模型中的条件依赖结构。然而，仅报告估计图的点估计值会因缺乏不确定性估计而导致可重复性较差。在心理学等领域，可重复性不足是一个主要问题，因此对能够解决该问题的方法需求日益增长。本文聚焦于高斯图模型，提出了一种选择性推断方法，为精度矩阵中选中的（非零）项附加不确定性估计，并决定估计的边中哪些应包含在图内。该方法对边的选择进行了精确调整，将其与随机矩阵的Wishart密度相乘后，可实现有效的选择性推断。通过引入外部添加的随机化变量，该调整易于计算——仅需计算选择事件概率，该概率等价于若干符号约束，且可在节点回归间解耦。通过仿真实验及一项针对心理健康研究的移动健康试验应用，我们证明该方法能带来更高的统计功效和更好的估计精度。