It is meaningful to detect outliers in traffic data for traffic management. However, this is a massive task for people from largescale database to distinguish outliers. In this paper, we present two methods: Kernel Smoothing Naïve Bayes (NB) method and Gaussian Mixture Model (GMM) method to automatically detect any hardware errors as well as abnormal traffic events in traffic data collected at a four-arm junction in Hong Kong. Traffic data was recorded in a video format, and converted to spatial-temporal (ST) traffic signals by statistics. The ST signals are then projected to a two-dimensional (2D) (x, y)-coordinate plane by Principal Component Analysis (PCA) for dimension reduction. We assume that inlier data are normal distributed. As such, the NB and GMM methods are successfully applied in OD (Outlier Detection) for traffic data. The kernel smooth NB method assumes the existence of kernel distributions in traffic data and uses Bayes' Theorem to perform OD. In contrast, the GMM method believes the traffic data is formed by the mixture of Gaussian distributions and exploits confidence region for OD. This paper would address the modeling of each method and evaluate their respective performances. Experimental results show that the NB algorithm with Triangle kernel and GMM method achieve up to 93.78% and 94.50% accuracies, respectively.