This paper presents a quasi-Bayesian model of subjective uncertainty in which beliefs which are represented by lower and upper probabilities qualified by numerical confidence weights. The representation is derived from a system of axioms of binary preferences which differs from standard axiom systems insofar as completeness is not assumed and transitivity is weakened. Confidence-weighted probabilities may be elicited through the acceptance of bets with limited stakes, a generalization of the operational method of de Finetti. The model is applicable to the reconciliation of inconsistent probability judgments and to the sensitivity analysis of Bayesian decision models.
@article{1176348888,
author = {Nau, Robert F.},
title = {Indeterminate Probabilities on Finite Sets},
journal = {Ann. Statist.},
volume = {20},
number = {1},
year = {1992},
pages = { 1737-1767},
language = {en},
url = {http://dml.mathdoc.fr/item/1176348888}
}
Nau, Robert F. Indeterminate Probabilities on Finite Sets. Ann. Statist., Tome 20 (1992) no. 1, pp. 1737-1767. http://gdmltest.u-ga.fr/item/1176348888/