Application of bayesian scientific approach to constructing the statistical estimations for solving metrological and measurement problems

Authors

  • Khayrullin Rustam Zinnatullivich Moscow State University of Civil Engineering, Yaroslavskoe shosse 26, 129337, Moscow, Russian Federation, Department of Applied Mathematics
  • Khaimuldinova Altyngul Kumashevna L.N. Gumilyov Eurasian National University, 13 Kazhymukan St., Nur-Sultan, Kazakhstan, Z01C0X0
  • Taimanova Gulnara Kabzhanovna L.N. Gumilyov Eurasian National University, 13 Kazhymukan St., Nur-Sultan, Kazakhstan, Z01C0X0
  • Sarsembayeva Tolkyn Erzhanovna S. Seifullin Kazakh Agrotechnical University, Zhenis avenue, 62, Nur-Sultan, Kazakhstan, 010011
  • Volkov Vladimir Sergeevich Voronezh State University of Forestry and Technologies named after G.F. Morozov 2/1 Lesokulturny lane, Voronezh, 394087, Russia
  • Shamina Svetlana Vladimirovna South Ural State Agrarian University, Troitsk, Chelyabinsk region, Gagarin str., 13, 457100
  • Lyalin Evgenij Aleksandrovich Perm State Agro-Technological University, 113, Geroev Khasana Street, Perm, Russia, 614025
  • Kabanov Oleg Vladimirovich Ogarev Mordovia State University, Russia, Republic of Mordovia, Saransk, 430005, bolshevitskaya street 68

DOI:

https://doi.org/10.5377/nexo.v34i04.12666

Keywords:

measurement accuracy, Bayesian scientific approach, a posteriori information, metrological and measurement problems

Abstract

Nowadays, constructing effective statistical estimates with a limited amount of statistical information constitutes a significant practical problem. The article is devoted to applying the Bayesian scientific approach to the construction of statistical estimates of the parameters of the laws of distribution of random variables. Five distribution laws are considered: The Poisson law, the exponential law, the uniform law, the Pareto law, and the ordinary law. The concept of distribution laws that conjugate with the observed population was introduced and used. It is shown that for considered distribution laws, the parameters of the laws themselves are random variables and obey the typical law, gamma law, gamma - normal law, and Pareto law. Recalculation formulas are obtained to refine the parameters of these laws, taking into account posterior information. If we apply the recalculation formulas several times in a row, we will get some convergent process. Based on a converging process, it is possible to design a process for self-learning a system or self-tuning a system. The developed scientific approach was applied to solve the measuring problems for the testing measuring devices and technical systems. The results of constructing point estimates and constructing interval estimates for these laws' parameters are given. The results of comparison with the corresponding statistical estimates constructed by the classical maximum likelihood method are presented.

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Published

2021-10-28

How to Cite

Rustam Zinnatullivich, K. ., Altyngul Kumashevna, K. ., Gulnara Kabzhanovna, T. ., Tolkyn Erzhanovna, S. ., Sergeevich, V. V. ., Vladimirovna, S. S. ., Evgenij Aleksandrovich, L. ., & Vladimirovich, K. O. . (2021). Application of bayesian scientific approach to constructing the statistical estimations for solving metrological and measurement problems . Nexo Scientific Journal, 34(04), 1301–1321. https://doi.org/10.5377/nexo.v34i04.12666

Issue

Vol. 34 No. 04 (2021)

Section

Articles

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