Autonomous Vehicles (AVs) have the potential to save millions of lives by reducing traffic deaths and accidents. However, despite recent advances, AVs have not met safety standard expectations for a variety of reasons, key among them being the difficulty in certifying AV safety. The development of model-based methods is essential for achieving more explainable tools that provide better safety assurances, in contrast to popular data-dependent end-to-end learning methods. This paper introduces a model-based collision prediction method that uses discretized Gaussian processes for future vehicle position estimation. It can incorporate road layout information, statistical agent dynamics, and be coupled with any trajectory prediction module. The discretization of the space together with a single Normal random variable for each vehicle trajectory allows fast and efficient computation for real-time deployment and computational intensive applications, such as simulation and training of Deep Learning and Reinforcement Learning models. The method can be applied to various scenarios by the adjustment of the model parameters that control dynamics uncertainty. Two scenarios extracted from real data are used as case studies.