Outlier detection has attracted considerable interest in various areas. Existing outlier detection methods usually assume independence of the modeling errors among the data points but this assumption does not hold in a number of applications. In this paper we propose a probabilistic method for outlier detection and robust updating of linear regression problems involving correlated data. First, suspicious data points will be identified using the minimum volume ellipsoid method and the maximum trimmed likelihood method. Then, the outlierness of each suspicious data point will be determined according to the proposed outlier probability in consideration of possible correlation among the data points. The proposed method is assessed and validated through simulated and real data.