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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Official URL: http://dx.doi.org/10.1016/j.jcp.2007.07.032

## Abstract

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 |
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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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