Upper and Lower Probabilities Induced by a Multivalued Mapping

1967/04/01 by A. P. Dempster · 42 citations
Computer Science · Mathematics · #Bayesian Modeling and Causal Inference #Advanced Statistical Methods and Models

paper · pdf · doi:10.1214/aoms/1177698950

Abstract

A multivalued mapping from a space X to a space S carries a probability measure defined over subsets of X into a system of upper and lower probabilities over subsets of S. Some basic properties of such systems are explored in Sections 1 and 2. Other approaches to upper and lower probabilities are possible and some of these are related to the present approach in Section 3. A distinctive feature of the present approach is a rule for conditioning, or more generally, a rule for combining sources of information, as discussed in Sections 4 and 5. Finally, the context in statistical inference from which the present theory arose is sketched briefly in Section 6.

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