In routine oncologic positron emission tomography (PET), dynamic information is discarded by time-averaging the signal to produce static images of the “standardised uptake value” (SUV). Defining functional volumes of interest (VOIs) in terms of SUV is flawed, as values are affected by confounding factors and the chosen time window, and SUV images are not sensitive to functional heterogeneity of pathological tissues. Also, SUV iso-contours are highly affected by the choice of threshold and no threshold, or other SUV-based segmentation method, is universally accepted for a given VOI type. Gaussian Process (GP) time series models describe macro-scale dynamic behavior arising from countless interacting micro-scale processes, as is the case for PET signals from heterogeneous tissue. We use GPs to model time-activity curves (TACs) from dynamic PET and to define functional volumes for PET oncology. Probabilistic methods of tissue discrimination are presented along with novel contouring methods for functional VOI segmentation. We demonstrate the value of GP models for voxel classification and VOI contouring of diseased and metastatic tissues with functional heterogeneity in prostate PET. Classification experiments reveal superior sensitivity and specificity over SUV calculation and a TAC-based method proposed in recent literature. Contouring experiments reveal differences in shape between gold-standard and GP VOIs and correlation with kinetic models shows that the novel VOIs contain extra clinically relevant information compared to SUVs alone. We conclude that the proposed models offer a principled data analysis technique that improves on SUVs for oncologic VOI definition. Continuing research will generalize GP models for different oncology tracers and imaging protocols with the ultimate goal of clinical use including treatment planning.