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Published in:
2012 | OriginalPaper | Chapter
Commentary by Victor M. Panaretos
Authors : Peter Guttorp, David Brillinger
Published in: Selected Works of David Brillinger
Publisher: Springer New York
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David began working on this paper while he held appointments at Princeton and Bell Labs, and completed it at the London School of Economics. He recalls (Panaretos [16]) that his motivation to consider this problem came from Don Fraser's program of
structural probability
, and in particular from the issue of formalising aspects of Fisher's
fiducial probability.
A particular example that David had in mind was that of the correlation coefficient: could Fraser's results be used to show that Fisher's fiducial distribution (Fisher [7]) can be obtained as a Bayesian posterior for some prior - as is often the case when a unique sufficient statistic exists? Lindley [15] had proved that, in the real case, a fiducial distribution would arise as a posterior if and only if the statistical problem were invariant, and so David set out to find conditions for invariance.