Road traffic sensors provide rich multivariable datastreams about the current traffic conditions. Occasionally, there are unusual traffic events (such as accidents, jams, and severe weather) that disrupt the expected road traffic conditions. Detecting the occurrence of such events in an online and real-time manner is useful to drivers in planning their routes and in the management of the transportation infrastructure. We propose a new method for detecting traffic events that impact road traffic conditions by extending the Bayesian robust principal component analysis (RPCA) approach. Our method couples multiple traffic datastreams so that they share a certain sparse structure. This sparse structure is used to localize traffic events in space and time. The traffic datastreams are measurements of different physical quantities (e.g., traffic flow and road occupancy) by different nearby sensors. Our proposed method processes datastreams in an incremental way with small computational cost; hence, it is suitable to detect events in an online and real-time manner. We experimentally analyze the detection performance of the proposed coupled Bayesian RPCA (BRPCA) using real data from loop detectors on the Minnesota I-494. We find that our method significantly improves the detection accuracy when compared with the traditional PCA and noncoupled BRPCA.