Summary
For an Euclidean groupG acting freely on the parameter space, we derive, among several noninformative priors, the reference priors of Berger-Bernardo and Chang-Eaves for our parameter of interest θ1, a scalar maximal invariant parametric function. Identifying the nuisance parameter vector with the group element, we derive a simple structure of the information matrix which is used to obtain different noninformative priors. We compare these priors using the marginalization paradox and the probability-matching criteria. The Chang-Eaves and the Berger-Bernardo reference priors appear to be the most attractive choice. Several illustrative examples are considered.
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Datta, G.S., Ghosh, J.K. Noninformative priors for maximal invariant parameter in group models. Test 4, 95–114 (1995). https://doi.org/10.1007/BF02563105
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DOI: https://doi.org/10.1007/BF02563105