DILATION FOR SETS OF PROBABILITIES

Suppose that a probability measure P is known to lie in a set of proba bility measures M. Upper and lower bounds on the probability of any ev ent may then be computed. Sometimes, the bounds on the probability of an event A conditional on an event B may strictly contain the bounds o n the unconditional probability of A. Surprisingly, this might happen for every B in a partition B. If so, we say that dilation has occurred . In addition to being an interesting statistical curiosity, this coun terintuitive phenomenon has important implications in robust Bayesian inference and in the theory of upper and lower probabilities. We inves tigate conditions under which dilation occurs and we study some of its implications. We characterize dilation immune neighborhoods of the un iform measure.