A NOTE ON THE ORTHOGONAL REPARAMETRIZATION IN BAYESIAN INFERENCE FOR THE EXTREME VALUE DISTRIBUTION
Josemar RODRIGUES[1]
Francisco LOUZADA NETO[2]
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ABSTRACT: Consider the problem of
inference about the scale parameter j
in presence of location parameter f
under the extreme value distribution. In a Bayesian framework, the marginal
posterior and the profile posterior may be of interest. In this paper, using
the Jeffreys prior density and the Laplace approximation, we show that these
posteriors are invariant under the orthogonal reparametrization (COX &
REID, 1987) adopted for the location parameter f .
Also, from the data generated by the extreme value distribution, we show that
the marginal and profile posteriors do not give conflicting information about
the scale parameter j.
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KEYWORDS: Marginal posterior;
profile posterior; orthogonality; reparametrization.