Translator Disclaimer
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

Abstract

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.

Citation

Download Citation

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

Information

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

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

Subjects:
Primary: 60A05

Rights: Copyright © 1982 Institute of Mathematical Statistics

JOURNAL ARTICLE
21 PAGES


SHARE
Vol.10 • No. 3 • September, 1982
Back to Top