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An Automatic Bayesian Procedure for Likelihoods with Shifted Origin

Neidha Nadal and Luis Raúl Pericchi
Journal of the Royal Statistical Society. Series D (The Statistician)
Vol. 47, No. 2 (1998), pp. 323-332
Published by: Wiley for the Royal Statistical Society
Stable URL: http://www.jstor.org/stable/2988670
Page Count: 10
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
An Automatic Bayesian Procedure for Likelihoods with Shifted Origin
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Abstract

An automatic Bayesian method for analysing irregular likelihoods with shifted unknown origin is proposed. Our procedure makes use of Bayesian marginalization by integration of parameters and of a convenient grouped likelihood function. The method is illustrated for the Weibull 3 likelihood and for the difficult situation of a shifted power transformation. Atkinson, Pericchi and Smith developed a grouped likelihood procedure for the shifted power transformation and conjectured that grouping the likelihood should have beneficial effects for Bayesian inference also. In this paper this conjecture is shown to be correct. Moreover, by analysing two sets of data, it is illustrated that our Bayesian procedure is both more informative regarding the shifted origin and more robust with respect to the truncation factor than grouped likelihood methods that have previously been proposed.

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