We present an approach for segmenting low- and high-grade gliomas in multimodal magnetic resonance imaging volumes. The proposed approach is based on a hybrid generative-discriminative model. Firstly, a generative approach based on an Expectation-Maximization framework that incorporates a glioma growth model is used to segment the brain scans into tumor, as well as healthy tissue labels. Secondly, a gradient boosting multi-class classification scheme is used to refine tumor labels based on information from multiple patients. Lastly, a probabilistic Bayesian strategy is employed to further refine and finalize the tumor segmentation based on patient-specific intensity statistics from the multiple modalities. We evaluated our approach in 186 cases during the training phase of the BRAin Tumor Segmentation (BRATS) 2015 challenge and report promising results. During the testing phase, the algorithm was additionally evaluated in 53 unseen cases, achieving the best performance among the competing methods.