Note on the Linearity of Bayesian Estimates in the Dependent Case ()
Souad Assoudou,
Belkheir Essebbar
Department of Economics, Faculty of Law, Economics and Social Sciences, Hassan I University, Settat, Morocco.
Department of Mathematics and Computer Sciences, Faculty of Science, Mohammed V University, Rabat, Morocco.
DOI: 10.4236/am.2014.51006
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Abstract
This work deals with the relationship between the Bayesian and the
maximum likelihood estimators in case of dependent observations. In case of
Markov chains, we show that the Bayesian estimator of the transition probabilities
is a linear function of the maximum likelihood estimator (MLE).
Share and Cite:
S. Assoudou and B. Essebbar, "Note on the Linearity of Bayesian Estimates in the Dependent Case,"
Applied Mathematics, Vol. 5 No. 1, 2014, pp. 47-54. doi:
10.4236/am.2014.51006.
Conflicts of Interest
The authors declare no conflicts of interest.
References
[1]
|
P. Diaconis and D. Ylvisaker, “Conjugate Priors for Exponential Families,” The Annals of Statistics, Vol. 7, No. 2, 1979, pp. 269-281.
|
[2]
|
T. C. Lee, G. G. Judge and A. Zellner, “Maximum Likelihood and Bayesian Estimation of Transition Probabilities,” JASA, Vol. 63, No. 324, 1968, pp. 1162-1179.
|
[3]
|
S. Assoudou and B. Essebbar, “A Bayesian Model for Markov Chains via Jeffreys’ Prior,” Department of Mathematics and Computer Sciences, Faculté des Sciences of Rabat, Morocco, 2001.
|
[4]
|
C. Robert, “Méthode de Monte Carlo par Chanes de Markov,” Economica, Paris, 1996.
|