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On the iterated a posteriori distribution in Bayesian statistics
Author(s):
F.
Recker
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika,
vipusk 74
(2006).
Journal:
Theor. Probability and Math. Statist.
No. 74
(2007),
163-170.
MSC (2000):
Primary 62F15, 62C12
Posted:
July 5, 2007
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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:
-
- 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:
10.1090/S0094-9000-07-00705-3
PII:
S 0094-9000(07)00705-3
Keywords:
Bayesian inference,
a posteriori distribution
Received by editor(s):
15/AUG/2004
Posted:
July 5, 2007
Copyright of article:
Copyright
2007,
American Mathematical Society
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