Total Evidence and Learning with Imprecise Probabilities

Published in Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications, PMLR 147:161–168, 2021

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In dynamic learning, a rational agent must revise their credence about a question of interest in accordance with the total evidence available between the earlier and later times. We discuss situations in which an observable event $F$ that is sufficient for the total evidence can be identified, yet its probabilistic modeling cannot be performed in a precise manner. The agent may employ imprecise (IP) models of reasoning to account for the identified sufficient event, and perform change of credence or sequential decisions accordingly. Our proposal is illustrated with three case studies: the classic Monty Hall problem, statistical inference with non-ignorable missing data, and the use of forward induction in a two-person sequential game.