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Maximum a Posteriori Estimation for Markov Chains Based on Gaussian Markov Random Fields

Please always quote using this URN:urn:nbn:de:0296-matheon-10931
  • In this paper, we present a Gaussian Markov random field (GMRF) model for the transition matrices (TMs) of Markov chains (MCs) by assuming the existence of a neighborhood relationship between states, and develop the maximum a posteriori (MAP) estimators under different obser- vation conditions. Unlike earlier work on TM estimation, our method can make full use of the similarity between different states to improve the estimated accuracy, and the estimator can be performed very efficiently by solving a convex programming problem. In addition, we discuss the parameter choice of the proposed model, and introduce a Monte Carlo cross validation (MCCV) method. The numerical simulations of a diffusion process are employed to show the effectiveness of the proposed models and algorithms.

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Metadaten
Author:Hao Wu, Frank Noe
URN:urn:nbn:de:0296-matheon-10931
Referee:Christof Schütte
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2012/02/27
Release Date:2012/02/27
Institute:Research Center Matheon
Freie Universität Berlin
MSC-Classification:62-XX STATISTICS / 62Mxx Inference from stochastic processes / 62M05 Markov processes: estimation
Preprint Number:937
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