STATISTICAL INFERENCES BASED ON A SECOND-ORDER POSSIBILITY DISTRIBUTION

1 December 1997

journal article
research article
Published by Taylor & Francis in International Journal of General Systems

Vol. 26 (4) , 337-383
https://doi.org/10.1080/03081079708945189

Abstract

A new, general method of statistical inference is proposed. It encompasses all the coherent forms of statistical inference that can be derived from a Bayesian prior distribution, Bayesian sensitivity analysis or upper and lower prior probabilities. The method is to model prior uncertainty about statistical parameters in terms of a second-order possibility distribution (a special type of upper probability) which measures the plausibility of each conceivable prior probability distribution. This defines an imprecise hierarchical model. Two,applications are studied: the problem of robustifying Bayesian analyses by forming a neighbourhood of a Bayesian prior distribution, and the problem of combining prior opinions from different sources.

Keywords

This publication has 24 references indexed in Scilit:

An overview of robust Bayesian analysis
TEST, 1994
Sensitivity in Bayesian Statistics: The Prior and the Likelihood
Journal of the American Statistical Association, 1991
Possibility Theory
Published by Springer Nature ,1988
Robust Bayes and Empirical Bayes Analysis with $_\epsilon$-Contaminated Priors
The Annals of Statistics, 1986
Unreliable probabilities, risk taking, and decision making
Synthese, 1982
Robust Statistics
Published by Wiley ,1981
On solutions of minimax test problems for special capacities
Probability Theory and Related Fields, 1981
Fuzzy Sets and Decision Analysis
IEEE Transactions on Systems, Man, and Cybernetics, 1980
Minimax Tests and the Neyman-Pearson Lemma for Capacities
The Annals of Statistics, 1973
Theory of capacities
Annales de l'institut Fourier, 1954