Summary
The Jeffreys prior is well known to have the property of invariance under reparametrization. The reference prior, defined in Bernardo (1979) and Berger and Bernardo (1992c), does not always possess this property. For the most important types of reparametrization, however, the reference prior is invariant.
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Yang, Y. Invariance of the reference prior under reparametrization. Test 4, 83–94 (1995). https://doi.org/10.1007/BF02563104
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DOI: https://doi.org/10.1007/BF02563104