The Annals of Statistics

Fiducial Prediction and Semi-Bayesian Inference

A. Philip Dawid and Jinglong Wang

Full-text: Open access

Abstract

We investigate the problem of fiducial prediction for unobserved quantities within the framework of the functional model described previously by Dawid and Stone. It is supposed that these are related to a completely unknown parameter by means of a regular functional model, and that the observations are either given as known functions of the predictands, or are themselves related to them by means of a functional model. We develop algebraic conditions which allow the application of fiducial logic to the prediction problem, and explore the consequences of such an application--some of which appear unacceptable unless still stronger conditions are imposed. A reinterpretation of the fiducial prediction problem is given which can be applied to yield an inferential distribution for the unknown parameter in the presence of partial prior information, expressible as a functional hypermodel for the parameter, governed by a completely unknown hyperparameter. This solution agrees with the fiducial distribution when the hypermodel is vacuous and with the Bayes posterior distribution when the hyperparameter is fully known, but allows in addition for intermediate levels of partial prior knowledge.

Article information

Source
Ann. Statist., Volume 21, Number 3 (1993), 1119-1138.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349253

Digital Object Identifier
doi:10.1214/aos/1176349253

Mathematical Reviews number (MathSciNet)
MR1241260

Zentralblatt MATH identifier
0815.62001

JSTOR
links.jstor.org

Subjects
Primary: 62A30
Secondary: 62A15

Keywords
Fiducial inference functional model prediction Bayesian inference

Citation

Dawid, A. Philip; Wang, Jinglong. Fiducial Prediction and Semi-Bayesian Inference. Ann. Statist. 21 (1993), no. 3, 1119--1138. doi:10.1214/aos/1176349253. https://projecteuclid.org/euclid.aos/1176349253


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