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Research
Discussion Paper: 98-10
Reference priors for the general location-scale model - Carmen Fernandez and Mark Steel
The reference prior algorithm (Berger and
Bernardo 1992) is applied to multivariate location-scale models with any regular
sampling density, where we establish the irrelevance of the usual assumption of
Normal sampling if our interest is in either the location or the scale. This
result immediately extends to the linear regression model. On the other hand, an
essentially arbitrary step in the reference prior algorithm, namely the choice
of the nested sequence of sets in the parameter space is seen to play a role.
Our results lend an additional motivation to the often used prior proportional
to the inverse of the scale parameter, as it is found to be both the
independence Jeffreys' prior and the reference prior under variation
independence in the sequence of sets, for any choice of the sampling density.
However, if our parameter of interest is not a one-to-one transformation of
either location or scale, the choice of the sampling density is generally shown
to intervene.
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