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Forward-reverse expectation-maximization algorithm for Markov chains: convergence and numerical analysis

Part of: Numerical analysis in abstract spaces Probabilistic methods, simulation and stochastic differential equations

Published online by Cambridge University Press:  26 July 2018

Christian Bayer ,
Hilmar Mai  and
John Schoenmakers
Christian Bayer*
Affiliation:
Weierstrass Institute for Applied Analysis and Stochastics
Hilmar Mai*
Affiliation:
Deutsche Bank AG
John Schoenmakers*
Affiliation:
Weierstrass Institute for Applied Analysis and Stochastics
*
* Postal address: Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117 Berlin, Germany.
** Postal address: Deutsche Bank AG, Otto-Suhr-Allee 16, 10585 Berlin, Germany.
* Postal address: Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117 Berlin, Germany.
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Abstract

We develop a forward-reverse expectation-maximization (FREM) algorithm for estimating parameters of a discrete-time Markov chain evolving through a certain measurable state-space. For the construction of the FREM method, we develop forward-reverse representations for Markov chains conditioned on a certain terminal state. We prove almost sure convergence of our algorithm for a Markov chain model with curved exponential family structure. On the numerical side, we carry out a complexity analysis of the forward-reverse algorithm by deriving its expected cost. Two application examples are discussed.

Keywords

Expectation-maximization algorithmMarkov chain estimationforward-reverse representationmaximum likelihood estimationMonte Carlo simulation

MSC classification

Primary: 65C05: Monte Carlo methods
Secondary: 65J20: Improperly posed problems; regularization
Type
Original Article
Information
Advances in Applied Probability , Volume 50 , Issue 2 , June 2018 , pp. 621 - 644
Copyright
Copyright © Applied Probability Trust 2018 

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