Abstract
For an invariant statistical model we consider the induced right Haar prior distribution and the resulting right Haar posterior. Using this posterior distribution, HPD (highest posterior density) regions of constant posterior probability are constructed and shown to exhibit probability matching. Further, HPD regions for equivariant functions of the parameter are also shown to exhibit probability matching. A number of examples are considered.
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Acknowledgements
Portions of M. L. Eaton’s research were supported by a grant from the University of Minnesota Retirees Association, Office of the Vice President for Research at the University of Minnesota.
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Eaton, M.L., Sudderth, W.D. Invariance, model matching and probability matching. Sankhya A 74, 170–193 (2012). https://doi.org/10.1007/s13171-012-0018-4
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DOI: https://doi.org/10.1007/s13171-012-0018-4