Fiducial Distributions and Bayes' Theorem

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ID: 296934
1958
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Abstract
SUMMARY 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.
Reference Key
openalex_W2904579171 Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors D. V. Lindley
Journal Journal of the Royal Statistical Society Series B (Statistical Methodology)
Year 1958
DOI
10.1111/j.2517-6161.1958.tb00278.x
URL
https://doi.org/10.1111/j.2517-6161.1958.tb00278.x
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