Repository: Freie Universität Berlin, Math Department

Generator Estimation of Markov Jump Processes

Metzner, Ph. and Dittmer, E. and Jahnke, T. and Schütte, Ch. (2007) Generator Estimation of Markov Jump Processes. J. Comp. Phys., 227 (1). pp. 353-375.

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Estimating the generator of a continuous-time Markov jump process based on incomplete data is a problem which arises in various applications ranging from machine learning to molecular dynamics. Several methods have been devised for this purpose: a quadratic programming approach (cf. [D.T. Crommelin, E. Vanden-Eijnden, Fitting timeseries by continuous-time Markov chains: a quadratic programming approach, J. Comp. Phys. 217 (2006) 782–805]), a resolvent method (cf. [T. Müller, Modellierung von Proteinevolution, PhD thesis, Heidelberg, 2001]), and various implementations of an expectation-maximization algorithm ([S. Asmussen, O. Nerman, M. Olsson, Fitting phase-type distributions via the EM algorithm, Scand. J. Stat. 23 (1996) 419–441; I. Holmes, G.M. Rubin, An expectation maximization algorithm for training hidden substitution models, J. Mol. Biol. 317 (2002) 753–764; U. Nodelman, C.R. Shelton, D. Koller, Expectation maximization and complex duration distributions for continuous time Bayesian networks, in: Proceedings of the twenty-first conference on uncertainty in AI (UAI), 2005, pp. 421–430; M. Bladt, M. Sørensen, Statistical inference for discretely observed Markov jump processes, J.R. Statist. Soc. B 67 (2005) 395–410]). Some of these methods, however, seem to be known only in a particular research community, and have later been reinvented in a different context. The purpose of this paper is to compile a catalogue of existing approaches, to compare the strengths and weaknesses, and to test their performance in a series of numerical examples. These examples include carefully chosen model problems and an application to a time series from molecular dynamics.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
Department of Mathematics and Computer Science > Institute of Mathematics > BioComputing Group
ID Code:35
Deposited By: Admin Administrator
Deposited On:03 Jan 2009 20:20
Last Modified:03 Mar 2017 14:39

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