Note on the Linearity of Bayesian Estimates  in the Dependent Case

Souad Assoudou; Belkheir Essebbar

doi:10.4236/am.2014.51006

Home > Journals > Physics & Mathematics > AM

AM> Vol.5 No.1, January 2014

Share This Article:

Open Access

Note on the Linearity of Bayesian Estimates in the Dependent Case

Abstract Full-Text HTML XML

Download as PDF (Size:249KB) PP. 47-54

DOI: 10.4236/am.2014.51006 2,715 Downloads 3,972 Views

Author(s) Leave a comment

Souad Assoudou, Belkheir Essebbar

Affiliation(s)

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.

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).

KEYWORDS

Bayes Estimator; Maximum Likelihood Estimator; Markov Chain; Transition Probabilities; Jeffreys’ Prior; Multivariate Beta Prior; MCMC

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

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.

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.