The reference prior algorithm (Berger and Bernardo, 1992) is applied to location- scale models with any regular sampling density. A number of two-sample problems is analyzed in this general context, extending the di erence, ratio and product of Normal means problems outside Normality, while explicitly considering possibly di erent sizes for each sample. Since the reference prior turns out to be improper in all cases, we examine existence of the resulting posterior distribution and its moments under sampling from scale mixtures of Normals. In the context of an empirical example, it is shown that a reference posterior analysis is numerically feasible and can display some sensitivity to the actual sampling distributions. This illustrates the practical importance of questioning the Normality assumption.
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Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number
104.
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