Bayes Factor (BF) is one of the tools used in Bayesian analysis for model selection. The predictive BF finds application in detecting outliers, which are relevant sources of estimation and forecast errors. An efficient framework for outlier detection is provided and purposely designed for large multidimensional datasets. Online detection and analytical tractability guarantee the procedure's efficiency. The proposed sequential Bayesian monitoring extends the univariate setup to a matrix--variate one. Prior perturbation based on power discounting is applied to obtain tractable predictive BFs. This way, computationally intensive procedures used in Bayesian Analysis are not required. The conditions leading to inconclusive responses in outlier identification are derived, and some robust approaches are proposed that exploit the predictive BF's variability to improve the standard discounting method. The effectiveness of the procedure is studied using simulated data. An illustration is provided through applications to relevant benchmark datasets from macroeconomics and finance.

翻译：贝叶斯因子（BF）是贝叶斯分析中用于模型选择的工具之一。预测性贝叶斯因子在检测异常值方面具有重要应用，这些异常值是导致估计和预测误差的关键来源。本文提出了一种专门针对大规模多维数据集设计的异常值检测高效框架。在线检测机制与解析可处理性保证了该方法的执行效率。所提出的序贯贝叶斯监测方法将单变量框架扩展至矩阵变量体系。通过基于幂折扣的先验扰动技术，获得了可解析处理的预测性贝叶斯因子。这种方法避免了贝叶斯分析中常见的计算密集型流程。本文推导了导致异常值识别结果不确定的条件，并提出若干鲁棒性改进方案——通过利用预测性贝叶斯因子的变异性来优化标准折扣方法。通过模拟数据验证了该方法的有效性，并借助宏观经济学与金融领域的典型基准数据集进行了应用展示。