Conditioning, kinematics, and exchangeability (1988)
Richard C. Jeffrey · Cambridge University Press eBooks · 1992
PREVIEW The change (“conditioning”) from prior P to posterior Q = P ( | E ) is appropriate only if it changes no probabilities conditionally on E . Under similar conditions a generalization of conditioning (“probability kinematics”) is appropriate when Q(E) < 1. That generalization is pretty nearly equivalent to ordinary conditioning on the extraordinary proposition that Q(E) has a certain value. Whether or not generalized conditioning is sensitive to the order in which successive changes are made depends on how the changes are set, e.g., by probabilities, or by ratios of probabilities. In a finitistic framework, simple and generalized (“partial”) exchangeability are characterized and related to probability kinematics. CONDITIONING Sometimes an experiment or observation is adequately represented by partitioning the sample space in such a way as to satisfy both of the following conditions. (1) Certainty. Observing the outcome drives your probability for some cell E of the partitioning to 1 . (2) Sufficiency. Probabilities conditioned on E remain unchanged .