What question did this study set out to answer?

The aim is to determine conditions under which fiducial distributions correspond to Bayes' distributions in statistics.

January 1, 1958Journal of the Royal Statistical Society Series B (Statistical Methodology)

Fiducial Distributions and Bayes' Theorem

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The aim is to determine conditions under which fiducial distributions correspond to Bayes' distributions in statistics.
Establish necessary and sufficient conditions for fiducial distribution of a parameter, given a random variable.
Extend prior results from Grundy’s 1956 work.
Investigate the condition in the context of the exponential family.
Condition (A) is identified as essential for fiducial and Bayesian arguments to align.
The fiducial argument is deemed inconsistent if condition (A) is not met in the presence of a single sufficient statistic.
When condition (A) is satisfied, fiducial reasoning equates to Bayesian reasoning using a uniform prior.

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Implication

This note establishes necessary conditions for fiducial distributions to align with Bayesian principles, suggesting implications for statistical analysis.

Cite This Study

D. V. Lindley (1958) studied this question.

synapsesocial.com/papers/69d8a8df945c639271beda96 https://doi.org/10.1111/j.2517-6161.1958.tb00278.x

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Implication

This note establishes necessary conditions for fiducial distributions to align with Bayesian principles, suggesting implications for statistical analysis.

Fiducial Distributions and Bayes' Theorem

Key Points

Discussion

Implication

Cite This Study

Fiducial Distributions and Bayes' Theorem

Key Points

Discussion

Implication

Cite This Study

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