Invariance of Posterior Distributions under Reparametrization

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. AMS (2000) subject classification. 62F15.