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September, 1993 Dilation for Sets of Probabilities
Teddy Seidenfeld, Larry Wasserman
Ann. Statist. 21(3): 1139-1154 (September, 1993). DOI: 10.1214/aos/1176349254

Abstract

Suppose that a probability measure $P$ is known to lie in a set of probability measures $M$. Upper and lower bounds on the probability of any event may then be computed. Sometimes, the bounds on the probability of an event $A$ conditional on an event $B$ may strictly contain the bounds on the unconditional probability of $A$. Surprisingly, this might happen for every $B$ in a partition $\mathscr{B}$. If so, we say that dilation has occurred. In addition to being an interesting statistical curiosity, this counterintuitive phenomenon has important implications in robust Bayesian inference and in the theory of upper and lower probabilities. We investigate conditions under which dilation occurs and we study some of its implications. We characterize dilation immune neighborhoods of the uniform measure.

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Teddy Seidenfeld. Larry Wasserman. "Dilation for Sets of Probabilities." Ann. Statist. 21 (3) 1139 - 1154, September, 1993. https://doi.org/10.1214/aos/1176349254

Information

Published: September, 1993
First available in Project Euclid: 12 April 2007

zbMATH: 0796.62005
MathSciNet: MR1241261
Digital Object Identifier: 10.1214/aos/1176349254

Subjects:
Primary: 62F15
Secondary: 62F35

Rights: Copyright © 1993 Institute of Mathematical Statistics

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Vol.21 • No. 3 • September, 1993
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