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Bayesian inference for Markov chains

Part of: Inference from stochastic processes Limit theorems

Published online by Cambridge University Press:  14 July 2016

Peter Eichelsbacher  and
Ayalvadi Ganesh
Peter Eichelsbacher*
Affiliation:
Ruhr-Universität Bochum
Ayalvadi Ganesh*
Affiliation:
Microsoft Research
*
∗ Postal address: Fakultät für Mathematik, Ruhr-Universität Bochum, NA 3/68, D-44780 Bochum, Germany. Email address: [email protected]
∗∗ Postal address: Microsoft Research, 7 J. J. Thomson Avenue, Cambridge CB3 0FB, UK.
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Abstract

We consider the estimation of Markov transition matrices by Bayes’ methods. We obtain large and moderate deviation principles for the sequence of Bayesian posterior distributions.

Keywords

Markov chainsBayesian inferencelarge deviationsmoderate deviations

MSC classification

Primary: 60F10: Large deviations
Secondary: 62M05: Markov processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 39 , Issue 1 , March 2002 , pp. 91 - 99
Copyright
Copyright © Applied Probability Trust 2002 

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Footnotes

Research supported by ARC Grant 880 from the Anglo-German foundation.

References

[1]. Dembo, A., and Zeitouni, O. (1998). Large Deviations Techniques and Applications. Springer, New York.CrossRefGoogle Scholar
[2]. Eichelsbacher, P., and Ganesh, A. J. (2002). Moderate deviations for Bayes posteriors. To appear in Scand. J. Statist.Google Scholar
[3]. Ganesh, A. J., and O’Connell, N. (1999). An inverse of Sanov's theorem. Statist. Prob. Lett. 42, 201–206.Google Scholar
[4]. Ganesh, A. J., and O’Connell, N. (2000). A large deviation principle for Dirichlet posteriors. Bernoulli 6, 1021–1034.CrossRefGoogle Scholar
[5]. Ghosal, S., Ghosh, J. K., and Ramamoorthi, R. V. (1999). Consistency issues in Bayesian nonparametrics. In Asymptotics, Nonparametrics and Time Series, ed. Ghosh, S., Marcel Dekker, New York, pp. 639–667.Google Scholar
[6]. Ibragimov, I. A. and Haśminskiȋ, R. Z. (1981). Statistical Estimation: Asymptotic Theory. Springer, New York.CrossRefGoogle Scholar
[7]. Le Cam, L. M. (1973). Convergence of estimates under dimensionality restrictions. Ann. Statist. 22, 38–53.Google Scholar
[8]. Papangelou, F. (1996). Large deviations and the Bayesian estimation of higher-order Markov transition functions. J. Appl. Prob. 33, 18–27.CrossRefGoogle Scholar
[9]. Paschalidis, I. Ch., and Vassilaras, S. (1999). On estimating buffer overflow probabilities under Markov-modulated inputs. In Proc. 37th Annual Allerton Conf., 1999.Google Scholar