This paper proposes a fully Bayesian framework for node-level outlier detection in graph signals, where measurements are observed on the nodes of an underlying graph. Unlike traditional outlier detection methods, our approach accounts for the relational dependencies induced by the graph, identifying outliers that disrupt the underlying smoothness. We model the observed signal as a combination of a graph-smooth component, captured via an intrinsic Gaussian Markov random field (IGMRF) prior, and a sparse outlier component modeled by a spike-and-slab prior. A key advantage of the proposed method is its ability to provide principled uncertainty quantification by estimating the posterior probability that each node is an outlier, rather than enforcing a deterministic binary decision. To facilitate posterior inference, we develop an efficient Gibbs sampling algorithm. We demonstrate the effectiveness of the proposed method through simulation studies on various graph structures, as well as a real data analysis of PM2.5 levels in California, exploring their relationship with wildfire occurrences.

翻译：本文提出了一种用于图信号节点级异常检测的全贝叶斯框架，其中测量值在底层图的节点上被观测到。与传统的异常检测方法不同，我们的方法考虑了图所诱导的关系依赖性，识别出破坏底层平滑性的异常点。我们将观测信号建模为图平滑分量与稀疏异常分量之和，其中平滑分量通过内在高斯马尔可夫随机场先验捕获，异常分量通过尖峰-板先验建模。该方法的一个关键优势在于能够通过估计每个节点为异常的后验概率来提供原则性的不确定性量化，而非强制执行确定性的二元决策。为了便于后验推断，我们开发了一种高效的吉布斯采样算法。通过在不同图结构上的仿真研究，以及对加州PM2.5水平与野火发生关系的实际数据分析，我们证明了所提方法的有效性。