Bayesian Outlier Detection for Matrix-variate Models

Anomalies in economic and financial data -- often linked to rare yet impactful events -- are of theoretical interest, but can also severely distort inference. Although outlier-robust methodologies can be used, many researchers prefer pre-processing strategies that remove outliers. In this work, an efficient sequential Bayesian framework is proposed for outlier detection based on the predictive Bayes Factor (BF). The proposed method is specifically designed for large, multidimensional datasets and extends univariate Bayesian model outlier detection procedures to the matrix-variate setting. Leveraging power-discounted priors, tractable predictive BF are obtained, thereby avoiding computationally intensive techniques. The BF finite sample distribution, the test critical region, and robust extensions of the test are introduced by exploiting the sampling variability. The framework supports online detection with analytical tractability, ensuring both accuracy and scalability. Its effectiveness is demonstrated through simulations, and three applications to reference datasets in macroeconomics and finance are provided.