Summary
It is shown that under fairly general conditions the Bayes procedure among the class of procedures invariant under a group of transformations which leave the statistical problem invariant, is really a Bayes or formal Bayes procedure with respect to a prior measure which is constructed from the right Haar measure on the group and the specified prior. This result is useful in problems where the principle of invariance is applied. Such cases, involving the two action problem or a selection and ranking problem are given as examples.
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Zidek, J.V. A representation of Bayes invariant procedures in terms of Haar measure. Ann Inst Stat Math 21, 291–308 (1969). https://doi.org/10.1007/BF02532257
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DOI: https://doi.org/10.1007/BF02532257