The fundamental conflict between the enormous space of adaptive streaming videos and the limited capacity for subjective experiment casts significant challenges to objective Quality-of-Experience (QoE) prediction. Existing objective QoE models either employ pre-defined parametrization or exhibit complex functional form, achieving limited generalization capability in diverse streaming environments. In this study, we propose an objective QoE model, namely, the Bayesian streaming quality index (BSQI), to integrate prior knowledge on the human visual system and human annotated data in a principled way. By analyzing the subjective characteristics towards streaming videos from a corpus of subjective studies, we show that a family of QoE functions lies in a convex set. Using a variant of projected gradient descent, we optimize the objective QoE model over a database of training videos. The proposed BSQI demonstrates strong prediction accuracy in a broad range of streaming conditions, evident by state-of-the-art performance on four publicly available benchmark datasets and a novel analysis-by-synthesis visual experiment.