This paper argues in favor of the thesis that two different concepts of conditional interval probability are needed, in order to serve the huge variety of tasks conditional probability has in the classical setting of precise probabilities. We compare the commonly used intuitive concept of conditional interval probability with the canonical concept, and see, in particular, that the canonical concept is the appropriate one to generalize the idea of transition kernels to interval probability: only the canonical concept allows reconstruction of the original interval probability from the marginals and conditionals, as well as the powerful formulation of Bayes Theorem.
Keywords. Conditional interval probability, intuitive concept of conditional interval probability, canonical concept of conditional interval probability, conditioning, updating, Theorem of Total Probability, Markov chains, Bayes' Theorem, decision theory
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Dep. of Statistics
D 80539 Muenchen
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