Fiducial and Posterior Sampling

Gunnar Taraldsen and Bo H. Lindqvist

Communications in Statistics - Theory and Methods, 2015, vol. 44, issue 17, 3754-3767

Abstract: The fiducial coincides with the posterior in a group model equipped with the right Haar prior. This result is generalized here. For this the underlying probability space of Kolmogorov is replaced by a σ-finite measure space and fiducial theory is presented within this frame. Examples are presented that demonstrate that this also gives good alternatives to existing Bayesian sampling methods. It is proved that the results provided here for fiducial models imply that the theory of invariant measures for groups cannot be generalized directly to loops: there exist a smooth one-dimensional loop where an invariant measure does not exist.

Date: 2015
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DOI: 10.1080/03610926.2013.823207

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