Dynamic Precise and Imprecise Probability Kinematics

We introduce a new method for updating subjective beliefs based on Jeffrey's rule of conditioning, called dynamic (precise) probability kinematics (DPK). We also give its generalization in order to work with sets of probabilities, called dynamic imprecise probability kinematics (DIPK). Updating a set of probabilities may be computationally costly. To this end, we provide bounds for the lower probability associated with the updated probability set, characterizing the set completely. The behavior of the updated sets of probabilities are studied, including contraction, dilation, and sure loss. We discuss the application of DPK and DIPK to survey sampling studies in which coarse and imprecise observations are anticipated.