This paper presents a method for detection of cerebral white matter hyperintensities (WMH) based on run-time PD-, T1-, and T2-weighted structural magnetic resonance (MR) images of the brain along with labeled training examples. Unlike most prior approaches, the method is able to reliably detect WMHs in elderly brains in the absence of fluid-attenuated (FLAIR) images. Its success is due to the learning of probabilistic models of WMH spatial distribution and neighborhood dependencies from ground-truth examples of FLAIR-based WMH detections. These models are combined with a probabilistic model of the PD, T1, and T2 intensities of WMHs in a Markov Random Field (MRF) framework that provides the machinery for inferring the positions of WMHs in novel test images. The method is shown to accurately detect WMHs in a set of 114 elderly subjects from an academic dementia clinic. Experiments show that standard off-the-shelf MRF training and inference methods provide robust results, and that increasing the complexity of neighborhood dependency models does not necessarily help performance. The method is also shown to perform well when training and test data are drawn from distinct scanners and subject pools.