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September, 1982 Towards a Frequentist Theory of Upper and Lower Probability
Peter Walley, Terrence L. Fine
Ann. Statist. 10(3): 741-761 (September, 1982). DOI: 10.1214/aos/1176345868


We present elements of a frequentist theory of statistics for concepts of upper and lower (interval-valued) probability (IVP), defined on finite event algebras. We consider IID models for unlinked repetitions of experiments described by IVP and suggest several generalizations of standard notions of independence, asymptotic certainty and estimability. Instability of relative freqencies is favoured under our IID models. Moreover, generalizations of Bernoulli's Theorem give some justification for the estimation of an underlying IVP mechanism from fluctuations of relative frequencies. Our results indicate that an objectivist, frequency- or propensity-oriented, view of probability does not necessitate an additive probability concept, and that IVP models can represent a type of indeterminacy not captured by additive probability.


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Peter Walley. Terrence L. Fine. "Towards a Frequentist Theory of Upper and Lower Probability." Ann. Statist. 10 (3) 741 - 761, September, 1982.


Published: September, 1982
First available in Project Euclid: 12 April 2007

zbMATH: 0488.62004
MathSciNet: MR663429
Digital Object Identifier: 10.1214/aos/1176345868

Primary: 60A05

Keywords: Bernoulli's Theorem , independence , interval-valued probability , Non-additive probability , propensities , unstable relative frequencies , upper and lower envelopes , Upper and lower probability

Rights: Copyright © 1982 Institute of Mathematical Statistics

Vol.10 • No. 3 • September, 1982
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