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On meta-level time scales, anomalous trajectories can signify target intent through their shape and eventual destination. Such trajectories exhibit complex spatial patterns and have well defined destinations with long-range dependencies implying that Markov (random-walk) models are unsuitable. How can estimated target tracks be used to detect anomalous trajectories such as circling a building or going past a sequence of checkpoints? This paper develops context-free grammar models and reciprocal Markov models (one dimensional Markov random fields) for modeling spatial trajectories with a known end point. The intent of a target is assumed to be a function of the shape of the trajectory it follows and its intended destination. The stochastic grammar models developed are concerned with trajectory shape classification while the reciprocal Markov models are used for destination prediction. Towards this goal, Bayesian signal processing algorithms with polynomial complexity are presented. The versatility of such models is illustrated with tracking applications in surveillance.