Improper regular conditional distributions

By Teddy Seidenfeld, Mark J. Schervish, Joseph B. Kadane. 2001

78 citations recorded by the source corpus.

Improper regular conditional distributions (rcd's) given a σ-field A have the following anomalous property. For sets A ∈ A, Pr(A |A) is not always equal to the indicator of A. Such a property makes the conditional probability puzzling as a representation of uncertainty. When rcd's exist and the σ-field A is countably generated, then almost surely the rcd is proper. We give sufficient conditions for an red to be improper in a maximal sense, and show that these conditions apply to the tail σ-field and the σfield of symmetric events.

Subfields: Management Science and Operations Research, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b72e505c3837d681b1945652e5487645321d50bf

Citations in the corpus

• What Conditional Probability Could Not Be (2003, unknown): “See also Seidenfeld et al. (2001).”