Fiducial Distributions and Bayes' Theorem
- 1 January 1958
- journal article
- research article
- Published by Oxford University Press (OUP) in Journal of the Royal Statistical Society Series B: Statistical Methodology
- Vol. 20 (1) , 102-107
- https://doi.org/10.1111/j.2517-6161.1958.tb00278.x
Abstract
x is a one‐dimensional random variable whose distribution depends on a single parameter θ. It is the purpose of this note to establish two results: (i) The necessary and sufficient condition for the fiducial distribution of θ, given x, to be a Bayes' distribution is that there exist transformations of x to u, and of θ to τ, such that τ is a location parameter for u. The condition will be referred to as (A). This extends some results of Grundy's (1956). (ii) If, for a random sample of any size from the distribution for x, there exists a single sufficient statistic for θ then the fiducial argument is inconsistent unless condition (A) obtains: And when it does, the fiducial argument is equivalent to a Bayesian argument with uniform prior distribution for τ. The note concludes with an investigation of (A) in the case of the exponential family.This publication has 1 reference indexed in Scilit:
- Fiducial Distributions and Prior Distributions: An Example in Which the Former Cannot be Associated with the LatterJournal of the Royal Statistical Society Series B: Statistical Methodology, 1956