Advanced technology in GPS and sensors enables us to track physical events, such as human movements and facility usage. Periodicity analysis from the recorded data is an important data mining task which provides useful insights into the physical events and enables us to report outliers and predict future behaviors. To mine periodicity in an event, we have to face real-world challenges of inherently complicated periodic behaviors and imperfect data collection problem. Specifically, the hidden temporal periodic behaviors could be oscillating and noisy, and the observations of the event could be incomplete. In this paper, we propose a novel probabilistic measure for periodicity and design a practical method to detect periods. Our method has thoroughly considered the uncertainties and noises in periodic behaviors and is provably robust to incomplete observations. Comprehensive experiments on both synthetic and real datasets demonstrate the effectiveness of our method.