Note on the Linearity of Bayesian Estimates in the Dependent Case


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).

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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.


[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.

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