Reference Priors Versus Reverse Reference Priors: The Role of Invariance

In this article, I investigate two classes of noninformative priors: the reference priors of Berger and Bernardo and the reverse reference priors attributed to J.K. Ghosh. Datta and Ghosh (1995) gave a simple condition under which reference priors agree with reverse reference priors. They also gave several examples showing agreement or disagreement between the two priors. I derive the reference priors and reverse reference priors for several reparametrization of one of these examples, examine the invariance properties of the different parametrizations, and observe an interesting relationship between priors and invariance properties.