On the iterated a posteriori distribution in Bayesian statistics
Author:
F. Recker
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
Full-text PDF Free Access
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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
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References
- J. A. Hartigan, Bayes Theory, Springer, New York, 1983. MR 715782 (85k:60008)
- W. Eberl and O. Moeschlin, Mathematische Statistik, de Gruyter, Berlin, 1982. MR 670752 (84e:62003)
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- T. Y. Young and T. W. Calvert, Classification, Estimation, and Pattern Recognition, Elsevier Science Publishers, Amsterdam, 1974. MR 0350975 (50:3467)
- O. Moeschlin, E. Grycko, C. Pohl, and F. Steinert, Experimental Stochastics, Springer, Berlin–New York, 1998.
- O. Moeschlin and F. Steinert, Bayessche Statistik, Birkhäuser, Basel, 1995.
- 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
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
