Abstract
In 1946, Sir Harold Jeffreys introduced a prior distribution whose density is the square root of the determinant of Fisher information. The motivation for suggesting this prior distribution is that the method results in a posterior that is invariant under reparametrization. For invariant statistical models when there is a transitive group action on the parameter space, it is shown that all relatively invariant priors have this “Jeffreys Invariance” property. However, this invariance may not prevail when using a subtle modification suggested by an alternative argument.
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Eaton, M.L., Sudderth, W.D. Invariance of posterior distributions under reparametrization. Sankhya 72, 101–118 (2010). https://doi.org/10.1007/s13171-010-0001-x
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DOI: https://doi.org/10.1007/s13171-010-0001-x