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Volume 59 >>> № 6 NOVEMBER — DECEMBER 2023

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UDC 519.21

O.S. Samosonok¹

¹ V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

AN ALGORITHM FOR ESTIMATING THE UNKNOWN PARAMETER
OF THE GIBBS DISTRIBUTION BASED ON THE METHOD
OF STOCHASTIC QUASI-GRADIENTS

Abstract. The author considers a practical algorithm for estimating an unknown parameter of a mathematical model of a Markov process with local interaction based on the Gibbs distribution. It is proposed to apply the method of stochastic quasi-gradients to the maximum likelihood function, which is constructed from the observations of the implementations of the Gibbs field. The obtained results have a wide application in the modeling of stochastic processes.

Keywords: Gibbs distribution, Maximum Likelihood Estimation, Markov random fields, stochastic quasigradient method, parameter estimation.

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REFERENCES

Knopov P.S., Samosyonok A.S. On some applied problems of Markov random processes with interaction. Kibernetika i sistemnyj analiz. 2011. N 3. P. 15–32.

Samosyonok A. S. Study of empirical estimates of the parameters of the Gibbs distribution obtained by the maximum likelihood method. Kibernetika i sistemnyj analiz. 2013. N 2. P. 178–187.

Ermoliev Yu.M. Methods of stochastic programming [in Russian]. Moscow: Nauka, 1976. 240 p.

Pflug G.Ch. Optimization of stochastic models. The interface between simulation and optimization. Dordrecht: Kluwer Academic Publishers, 1996. 382 p.

UDC 519.21

AN ALGORITHM FOR ESTIMATING THE UNKNOWN PARAMETER OF THE GIBBS DISTRIBUTION BASED ON THE METHOD OF STOCHASTIC QUASI-GRADIENTS

REFERENCES

AN ALGORITHM FOR ESTIMATING THE UNKNOWN PARAMETER
OF THE GIBBS DISTRIBUTION BASED ON THE METHOD
OF STOCHASTIC QUASI-GRADIENTS