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Theory of Probability and Mathematical Statistics

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On the iterated a posteriori distribution in Bayesian statistics


Author: F. Recker
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 74 (2006).
Journal: Theor. Probability and Math. Statist. 74 (2007), 163-170
MSC (2000): Primary 62F15, 62C12
DOI: https://doi.org/10.1090/S0094-9000-07-00705-3
Published electronically: July 5, 2007
MathSciNet review: 2336786
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Abstract | References | Similar Articles | Additional Information

Abstract: In theoretical considerations a Bayesian experiment consisting of many independently drawn samples is usually modeled by a product space. However, in some applications, as e.g. pattern recognition, the mathematical model is different. This model will be presented and a rigid measure-theoretic proof will be given showing that both models deliver the same a posteriori distribution.


References [Enhancements On Off] (What's this?)

  • 1. J. A. Hartigan, Bayes Theory, Springer, New York, 1983. MR 715782 (85k:60008)
  • 2. W. Eberl and O. Moeschlin, Mathematische Statistik, de Gruyter, Berlin, 1982. MR 670752 (84e:62003)
  • 3. L. LeCam, Asymptotic Methods in Statistical Decision Theory, Springer, New York, 1986. MR 856411 (88a:62004)
  • 4. L. LeCam, Asymptotics in Statistics, Springer, New York, 1990. MR 1066869 (92k:62050)
  • 5. P. Rao, Asymptotic Theory of Statistical Inference, John Wiley, New York, 1987. MR 874342 (88b:62001)
  • 6. T. Y. Young and T. W. Calvert, Classification, Estimation, and Pattern Recognition, Elsevier Science Publishers, Amsterdam, 1974. MR 0350975 (50:3467)
  • 7. O. Moeschlin, E. Grycko, C. Pohl, and F. Steinert, Experimental Stochastics, Springer, Berlin-New York, 1998.
  • 8. O. Moeschlin and F. Steinert, Bayessche Statistik, Birkhäuser, Basel, 1995.
  • 9. J. P. Florens, M. Mouchart, and J. M. Rolin, Elements of Bayesian Statistics, Marcel Dekker, New York, 1990. MR 1051656 (91g:62004)

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Additional Information

F. Recker
Affiliation: Department of Mathematics, University of Hagen, D-58084 Hagen, Germany
Email: Frank.Recker@FernUni-Hagen.de

DOI: https://doi.org/10.1090/S0094-9000-07-00705-3
Keywords: Bayesian inference, a posteriori distribution
Received by editor(s): August 15, 2004
Published electronically: July 5, 2007
Article copyright: © Copyright 2007 American Mathematical Society

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