This thesis describes a robust and efficient design of Student-t based Robust Spatio-Temporal Prediction, namely, St-RSTP, to provide estimation based on observations over spatio-temporal neighbors. It is crucial to many applications in geographical information systems, medical imaging, urban planning, economy study, and climate forecasting. The proposed St-RSTP is more resilient to outliers or other small departures from model assumptions than its ancestor, the Spatio-Temporal Random Effects (STRE) model. STRE is a statistical model with linear order complexity for processing large scale spatiotemporal data. However, STRE has been shown sensitive to outliers or anomaly observations. In our design, the St-RSTP model assumes that the measurement error follows Student's t-distribution, instead of a traditional Gaussian distribution. To handle the analytical intractable inference of Student's t model, we propose an approximate inference algorithm in the framework of Expectation Propagation (EP). Extensive experimental evaluations, based on both simulation and real-life data sets, demonstrated the robustness and the efficiency of our Student-t prediction model compared with the STRE model. / Master of Science