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Bayesian Inference under Ambiguity: Conditional Prior Belief Functions
Proceedings of the Tenth International Symposium on Imprecise Probability: Theories and Applications, PMLR 62:73-84, 2017.
Abstract
Bayesian inference under imprecise prior information is studied: the starting point is a precise strategy σ and a full B-conditional prior belief function Bel_B, conveying ambiguity in probabilistic prior information. In finite spaces, we give a closed form expression for the lower envelope \underline{P} of the class of full conditional probabilities dominating (Bel_B,σ) and, in particular, for the related “posterior probabilities”. The assessment (Bel_B,σ) is a coherent lower conditional probability in the sense of Williams and the characterized lower envelope \underline{P} coincides with its natural extension.