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Identification of Markov processes using statistical data

Keywords:

L.S. Kuravsky - Dr. Sc. (Eng.), Professor, Dean of the «Information technologies» Faculty, Moscow State University of Psychology and Education. E-mail: l.s.kuravsky@gmail.com P.A. Marmalyuk - Ph.D. (Eng.), Head of the Laboratory of Mathematical Psychology and Applied Software, Moscow State University of Psychology and Education. E-mail: pavel.marmalyuk@gmail.com G.A. Yuryev - Ph.D. (Phys.-Math.), Vice Dean of Academic Affairs of the «Information technologies» Faculty, Moscow State University of Psychology and Education. E-mail: nezdeshni@gmail.com P.N. Dumin - Programmer at the Laboratory of Mathematical Psychology and Applied Software, Moscow State University of Psychology and Education. E-mail: dumin.pn@gmail.com


A numerical technique for the identification of discrete-state continuous-time Markov models is presented in the paper. The details of the identification problem are presented in section 1. The developed technique is characterized by utilizing both initial approximations derived from observed data and estimates of minimized criterion sensitivity to small variations of identified parameters. A new feature of the proposed approach is improved running time of the applied combinatorial optimization algorithm achieved through replacing, at each iteration, of enumeration of various combinations of parameter values in the neighborhood of their current estimates by enumeration of values of only those parameters to which the minimized criterion is highly sensitive. Proposed approach is planned to be experimentally compared with a first order gradient method with adaptive steps described in section 2, which is traditionally applied for solving multivariate nonlinear optimization problems.
References:

 

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  3. Kuravskijj L.S., Margolis A.A., Marmaljuk P.A., JUrev G.A., Dumin P.N. Obuchaemye markovskie modeli v zadachakh optimizacii porjadka predjavlenija psikhologicheskikh testov // Nejjrokompjutery: razrabotka i primenenie. 2013. №4. S. 28–38.
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