Geodesic
On consistency of Bayes procedures
Teoriâ veroâtnostej i ee primeneniâ, Tome 47 (2002) no. 2, pp. 229-254

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For a wide class of statistical models with $\sigma$-finite priors, sufficient conditions for consistency of Bayes procedures for almost all values of the parameter are given. For a more restrictive class of invariant statistical models with some $\sigma$-finite priors, we give sufficient conditions for consistency of Bayes procedures for all values of the parameter. Particular cases of these invariant statistical models include the location model on a locally compact Polish group, rotation invariant families on the unit sphere in $\mathbf{R}^k$, and the scale-location model in $\mathbf{R}^k$.
Keywords: consistency, Bayes estimates, posterior distributions, invariant probability, statistical models.
Mots-clés : invariant Markov kernels 
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     author = {A. I. Lo and V. V. Sazonov},
     title = {On consistency of {Bayes} procedures},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {229--254},
     publisher = {mathdoc},
     volume = {47},
     number = {2},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2002_47_2_a1/}
}
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A. I. Lo; V. V. Sazonov. On consistency of Bayes procedures. Teoriâ veroâtnostej i ee primeneniâ, Tome 47 (2002) no. 2, pp. 229-254. http://geodesic.mathdoc.fr/item/TVP_2002_47_2_a1/