Refining expert based evaluation on the basis of a limited quantity of data

Simple item page
dc.citation.epage66
dc.citation.issue1
dc.citation.journalTitleУкраїнський журнал інформаційних технологій
dc.citation.spage58
dc.citation.volume1
dc.contributor.affiliationНаціональний університет “Львівська політехніка”
dc.contributor.affiliationLviv Polytechnic National University
dc.contributor.authorГрицюк, Юрій Іванович
dc.contributor.authorФернеза, О. Р.
dc.contributor.authorHrytsiuk, Yu. I.
dc.contributor.authorFerneza, O. R.
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2022-05-24T10:02:37Z
dc.date.available2022-05-24T10:02:37Z
dc.date.created2019-09-26
dc.date.issued2019-09-26
dc.description.abstractРозроблено методику уточнених експертних оцінок параметра розподілу ймовірностей випадкової величини на підставі обмеженого обсягу статистичних даних. Це дало змогу виявити найбільш інформативний канал передачі даних (кваліфікованого експерта) і отримати його достовірну оцінку. Встановлено, що аналіз та оброблення даних здійснюють із залученням відомих методик з теорії ймовірностей та математичної статистики, де нагромаджено значний теоретичний і практичний досвід. Математичну модель, яка описує стан деякого об'єкта, процесу чи явища, подано у вигляді точкової оцінки параметра розподілу ймовірностей випадкової величини, значення якого отримують на підставі малої вибірки. Проаналізовано сучасні підходи до статистичного оцінювання випадкової величини, найпоширенішим з яких є Байєсовський підхід. Встановлено, що найбільш значущим моментом Байєсового оцінювання невідомого параметра є призначення певної функції апріорної щільності розподілу ймовірностей випадкової величини. Ця функція має відповідати наявній попередній інформації про форму апріорного розподілу ймовірностей цієї величини. Розглянуто традиційний підхід до виявлення найбільш інформативного каналу передачі даних про стан об'єкта, перебіг процесу чи явища і відсікання інших – менш достовірних. Це здійснюють за допомогою так званого механізму редукторів ступенів свободи. Його основний недолік полягає в тому, що у відсічених каналах зв'язку може існувати деяка корисна інформація, яка не бере участі в процесі вироблення узгодженого рішення. Тому потрібно вводити механізми дискримінаторів ступенів свободи. Вони дадуть змогу всім каналам передачі даних брати участь в процесі підготовки рішення з вагомістю, яка відповідає найбільшому ступеню їх інформативності в поточній ситуації. Наведено ілюстративний приклад застосування розглянутих методів усереднення даних, у якому відображено результати розрахунків за ітераціями з використанням механізмів реалізації як редукторів, так і дискримінаторів ступенів свободи. Ці механізми відображають особливості реалізації ітераційних алгоритмів, характерних як для методів математичної статистики, так і для методів синергетичної системи усереднення даних.
dc.description.abstractA technique has been developed to refine expert based evaluation of the probability distribution parameter of a random variable based on a limited amount of statistical data. This made it possible to identify the most informative data transmission channel (the most qualified expert) and get its reliable assessment. It has been established that the analysis and processing of a limited amount of data is carried out using well-known techniques in probability theory and mathematical statistics, where significant theoretical and practical experience has been accumulated. A mathematical model that describes the state of an object, process, or phenomenon is presented as a point estimate of the probability distribution parameter of a random variable, the value of which is obtained on the basis of a small sample of data. The modern approaches to the statistical estimation of a random variable are analyzed, the most common of which is the Bayesian approach. It is established that the most significant moment of the Bayesian estimation of the unknown parameter of the probability distribution of a random variable is the appointment of a certain function of the a priori density of its distribution. This function should correspond to the available preliminary information on the shape of the a priori probability distribution of this quantity. The traditional approach to identifying the most informative channel for transmitting data on the state of an object, the course of a process or phenomenon, and cutting off others is less reliable. This is carried out using the so-called mechanism of reducers of degrees of freedom. Its main disadvantage is that in the cut-off data transmission channels, there may be some useful information that is not involved in the development of an agreed solution. Therefore, it is necessary to introduce mechanisms of discriminators of degrees of freedom. They allow all data transmission channels to participate in the decision-making process in terms of importance, which corresponds to the greatest degree of their information content in the current situation. An illustrative example of the application of the considered methods of averaging data is shown, which reflects the results of calculations by iterations using the implementation mechanisms of both reducers and discriminators of degrees of freedom. These mechanisms reflect the features of the implementation of iterative algorithms that are characteristic of both methods of mathematical statistics and methods of a synergetic system of averaging data.
dc.format.extent58-66
dc.format.pages9
dc.identifier.citationHrytsiuk Yu. I. Refining expert based evaluation on the basis of a limited quantity of data / Yu. I. Hrytsiuk, O. R. Ferneza // Український журнал інформаційних технологій. — Львів : Видавництво Львівської політехніки, 2019. — Том 1. — № 1. — С. 58–66.
dc.identifier.citationenHrytsiuk Yu. I. Refining expert based evaluation on the basis of a limited quantity of data / Yu. I. Hrytsiuk, O. R. Ferneza // Ukrainian Journal of Information Technology. — Lviv : Vydavnytstvo Lvivskoi politekhniky, 2019. — Vol 1. — No 1. — P. 58–66.
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/56875
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.relation.ispartofУкраїнський журнал інформаційних технологій, 1 (1), 2019
dc.relation.ispartofUkrainian Journal of Information Technology, 1 (1), 2019
dc.relation.references[1] Aizerman, M. A., Braverman, E. M., & Rozonoer, L. I. (1970). The method of potential functions in machine learning theory. Moscow: Science. 384 p. [In Russian].
dc.relation.references[2] Bakhrushin, V. E. (2006). Data Analysis: a tutorial. Zaporizhzhia: PG "Humanities", 128 p. [In Ukrainian].
dc.relation.references[3] Bakhrushin, V. E., & Ignahina, M. A. (2008). Application of statistical methods in processing the results of production control in metallurgy of semiconductors. System Technology, 3(56), Vol. 1, 3–7. [In Russian].
dc.relation.references[4] Botsula, M., & Morgun, I. (2008). The problem of quality examination of distance courses. Scientifical Journals of Vinnytsia National Technical University, 4, 1–7. Retrieved from: http://nbuv.gov.ua/e-iournals/vntu/2008-4/2008-4.files/uk/08mpbcme.uk.pdf. [In Ukrainian].
dc.relation.references[5] Brandt, Z. (2003). Data analysis: Statistical and Computational Methods for Scientists and Engineers. Moscow: Mir, AST, 686 p. [In Russian].
dc.relation.references[6] Gaskarov, D., & Shapovalov, V. I. (1978). Small sample. Moscow: Statistics, 248 p. [In Russian].
dc.relation.references[7] Gmurman, B. E. (2004). Guide to solving problems of the theory of probability and mathematical statistics. Moscow: Higher School, 404 p. [In Russian].
dc.relation.references[8] Gmurman, V. E. (2003). Probability theory and mathematical statistics. Moscow: Higher School, 479 p. [In Russian].
dc.relation.references[9] Gryciuk, Yu. I., & Grytsyuk, P. Yu. (2019). Contemporary problems of scientific evaluation of the application software quality. Scientific Bulletin of UNFU, 25(7), 284–294. https://doi.org/10.15421/40250745
dc.relation.references[10] Guter, R. S., & Reznikovskii, P. T. (1971). Programming and computational mathematics. Moscow: Science. Vol. 2, 273 p. [In Russian].
dc.relation.references[11] Hrytsiuk, Yu. I., & Andrushchakevych, O. T. (2018). Means for determining software quality by metric analysis methods. Scientific Bulletin of UNFU, 28(6), 159–171. https://doi.org/10.15421/40280631.
dc.relation.references[12] Hrytsiuk, Yu. I., & Buchkovska, A. Yu. (2017). Visualization of the Results of Expert Evaluation of Software Quality Using Polar Diagrams. Scientific Bulletin of UNFU, 27(10), 137–145. https://doi.org/10.15421/40271025
dc.relation.references[13] Hrytsiuk, Yu. I., & Grytsyuk, P. Yu. (2019). The methods of the specified points of the estimates of the parameter of probability distribution of the random variable based on a limited amount of data. Scientific Bulletin of UNFU, 29(2), 141–149. https://doi.org/10.15421/40290229
dc.relation.references[14] Hrytsiuk, Yu. I., & Nemova, E. A. (2018). Peculiarities of Formulation of Requirements to the Software. Scientific Bulletin of UNFU, 28(7), 135–148. https://doi.org/10.15421/40280727.
dc.relation.references[15] Kartavy, V., & Yarovaya, V. (2004). Mathematical Statistics. Kyiv: Professional, 484 p. [In Ukrainian].
dc.relation.references[16] Kobzar, A. I. (2006). Applied Mathematical Statistics. Moscow: Fizmatlit, 816 p. [In Russian].
dc.relation.references[17] Kolesnikov, A. A. (1994). Synergetic theory of management. Moscow: Energoatomisdat, 344 p. [In Russian].
dc.relation.references[18] Lagutin, M. B. (2007). Transparent mathematical statistics. Moscow: Binom, 472 p. [In Russian].
dc.relation.references[19] Mikitin, J. P. (2008). Programming model averaging method Noise. Bulletin of the National University "Lviv Polytechnic". Series: Computer Science and Information Technology, 629, 21–24. [In Ukrainian].
dc.relation.references[20] Morgun, I. (2011). The method of peer review software quality. Software Engineering: mater. Intern. nauk. and practical. Conf. graduate students, 2(6), 33–37. Vinnytsia. Retrieved from: http://jrnl.nau.edu.ua/index.php/IPZ/article/view/3086. [In Ukrainian].
dc.relation.references[21] Orlov, A. I. (2006). Applied Statistics. Moscow: Exam, 671 p. [In Russian].
dc.relation.references[22] Pleskach, V. L., & Zatonatska, T. (2011). Information systems and technology in enterprises: textbook. Kyiv: Knowledge. 718 p. Retrieved from: http://pidruchniki. com/1194121347734/informatika/analiz_yakosti_programnogo_ zabezpechennya#42. [In Ukrainian].
dc.relation.references[23] Protasov, K. V. (2005). Statistical analysis of experimental data. Moscow: Mir, 142 p. [In Russian].
dc.relation.references[24] Sage, E., & Mels, J. (1976). Estimation theory and its application in communication and management. Moscow: Communication, 496 p. [In Russian].
dc.relation.references[25] Shannon, K. (1963). Work on information theory and cybernetics. Moscow: Publishing House of Foreign Literature, 829 p. [In Russian].
dc.relation.references[26] Tolbatov, A. (1994). Mathematical Statistics and task optimization algorithms and programs. Kyiv: High School, 226 p. [In Ukrainian].
dc.relation.references[27] Tuluchenko, G. Y. (2008). Geometry computing templates bars of centric averaging method. Bulletin of the Zaporizhzhya National University, 1, 187–190. [In Ukrainian].
dc.relation.references[28] Turchin, V. (2006). Probability and Mathematical Statistics: Concepts, examples, problem. Dnepropetrovsk: Dniprovsky National University, 476 p. [In Ukrainian].
dc.relation.references[29] Vankovych, T.-N. M., Zinko, J. A., & Bozhenko, M. (2010). An averaging method for oscillating stochastic systems with quick phase. Bulletin of the National University "Lviv Polytechnic". Series: Dynamics, Durability and Design of Machines and Devices, 678, 11–14. [In Ukrainian].
dc.relation.references[30] Voronin, A. N. (2004). Method of interconnecting signals for bistatic radar small celestial bodies. System analysis and ma nagement: meas. rep. 9th International. Conf., (pp. 113–114). Moscow: Publishing house of the Moscow Aviation Institute. [In Russian].
dc.relation.references[31] Voronin, A. N. (2006). Synergistic methods of data aggregation. Cybernetics and Systems Analysis, 2, 24–30. [In Russian].
dc.relation.references[32] Voronin, A. N. (2014). Methods of data aggregation. Cybernetics and Systems Analysis, 50(5), 78–84. [In Russian].
dc.relation.references[33] Voronin, A. N., & Ziatdinov, J. K. (2013). Theory and practice of multi-criteria decisions: models, methods, implementation. Saarbrucken (Deutschland); Lambert Academic Publishing, 305 p. [In Russian].
dc.relation.references[34] Voronin, A. N., Ziatdinov, J. K., & Kulinskiy, M. V. (2011). Multicriteria task: models and methods: a monograph. Kyiv: NAU, 348 p. [In Russian].
dc.relation.references[35] Zhluktenko, V. I., & Nakonechny, S. (2000). Probability and Mathematical Statistics: training method. manual. In 2 parts. Part I. Probability. Kyiv: Kyiv National Economic University, 304 p. [In Ukrainian].
dc.relation.references[36] Zhluktenko, V. I., Nakonechny, S., & Savin, S. (2001). Probability and Mathematical Statistics: training method. manual. In 2 parts. Part II. Mathematical Statistics. Kyiv: Kyiv National Economic University, 336 p. [In Ukrainian].
dc.relation.referencesen[1] Aizerman, M. A., Braverman, E. M., & Rozonoer, L. I. (1970). The method of potential functions in machine learning theory. Moscow: Science. 384 p. [In Russian].
dc.relation.referencesen[2] Bakhrushin, V. E. (2006). Data Analysis: a tutorial. Zaporizhzhia: PG "Humanities", 128 p. [In Ukrainian].
dc.relation.referencesen[3] Bakhrushin, V. E., & Ignahina, M. A. (2008). Application of statistical methods in processing the results of production control in metallurgy of semiconductors. System Technology, 3(56), Vol. 1, 3–7. [In Russian].
dc.relation.referencesen[4] Botsula, M., & Morgun, I. (2008). The problem of quality examination of distance courses. Scientifical Journals of Vinnytsia National Technical University, 4, 1–7. Retrieved from: http://nbuv.gov.ua/e-iournals/vntu/2008-4/2008-4.files/uk/08mpbcme.uk.pdf. [In Ukrainian].
dc.relation.referencesen[5] Brandt, Z. (2003). Data analysis: Statistical and Computational Methods for Scientists and Engineers. Moscow: Mir, AST, 686 p. [In Russian].
dc.relation.referencesen[6] Gaskarov, D., & Shapovalov, V. I. (1978). Small sample. Moscow: Statistics, 248 p. [In Russian].
dc.relation.referencesen[7] Gmurman, B. E. (2004). Guide to solving problems of the theory of probability and mathematical statistics. Moscow: Higher School, 404 p. [In Russian].
dc.relation.referencesen[8] Gmurman, V. E. (2003). Probability theory and mathematical statistics. Moscow: Higher School, 479 p. [In Russian].
dc.relation.referencesen[9] Gryciuk, Yu. I., & Grytsyuk, P. Yu. (2019). Contemporary problems of scientific evaluation of the application software quality. Scientific Bulletin of UNFU, 25(7), 284–294. https://doi.org/10.15421/40250745
dc.relation.referencesen[10] Guter, R. S., & Reznikovskii, P. T. (1971). Programming and computational mathematics. Moscow: Science. Vol. 2, 273 p. [In Russian].
dc.relation.referencesen[11] Hrytsiuk, Yu. I., & Andrushchakevych, O. T. (2018). Means for determining software quality by metric analysis methods. Scientific Bulletin of UNFU, 28(6), 159–171. https://doi.org/10.15421/40280631.
dc.relation.referencesen[12] Hrytsiuk, Yu. I., & Buchkovska, A. Yu. (2017). Visualization of the Results of Expert Evaluation of Software Quality Using Polar Diagrams. Scientific Bulletin of UNFU, 27(10), 137–145. https://doi.org/10.15421/40271025
dc.relation.referencesen[13] Hrytsiuk, Yu. I., & Grytsyuk, P. Yu. (2019). The methods of the specified points of the estimates of the parameter of probability distribution of the random variable based on a limited amount of data. Scientific Bulletin of UNFU, 29(2), 141–149. https://doi.org/10.15421/40290229
dc.relation.referencesen[14] Hrytsiuk, Yu. I., & Nemova, E. A. (2018). Peculiarities of Formulation of Requirements to the Software. Scientific Bulletin of UNFU, 28(7), 135–148. https://doi.org/10.15421/40280727.
dc.relation.referencesen[15] Kartavy, V., & Yarovaya, V. (2004). Mathematical Statistics. Kyiv: Professional, 484 p. [In Ukrainian].
dc.relation.referencesen[16] Kobzar, A. I. (2006). Applied Mathematical Statistics. Moscow: Fizmatlit, 816 p. [In Russian].
dc.relation.referencesen[17] Kolesnikov, A. A. (1994). Synergetic theory of management. Moscow: Energoatomisdat, 344 p. [In Russian].
dc.relation.referencesen[18] Lagutin, M. B. (2007). Transparent mathematical statistics. Moscow: Binom, 472 p. [In Russian].
dc.relation.referencesen[19] Mikitin, J. P. (2008). Programming model averaging method Noise. Bulletin of the National University "Lviv Polytechnic". Series: Computer Science and Information Technology, 629, 21–24. [In Ukrainian].
dc.relation.referencesen[20] Morgun, I. (2011). The method of peer review software quality. Software Engineering: mater. Intern. nauk. and practical. Conf. graduate students, 2(6), 33–37. Vinnytsia. Retrieved from: http://jrnl.nau.edu.ua/index.php/IPZ/article/view/3086. [In Ukrainian].
dc.relation.referencesen[21] Orlov, A. I. (2006). Applied Statistics. Moscow: Exam, 671 p. [In Russian].
dc.relation.referencesen[22] Pleskach, V. L., & Zatonatska, T. (2011). Information systems and technology in enterprises: textbook. Kyiv: Knowledge. 718 p. Retrieved from: http://pidruchniki. com/1194121347734/informatika/analiz_yakosti_programnogo_ zabezpechennya#42. [In Ukrainian].
dc.relation.referencesen[23] Protasov, K. V. (2005). Statistical analysis of experimental data. Moscow: Mir, 142 p. [In Russian].
dc.relation.referencesen[24] Sage, E., & Mels, J. (1976). Estimation theory and its application in communication and management. Moscow: Communication, 496 p. [In Russian].
dc.relation.referencesen[25] Shannon, K. (1963). Work on information theory and cybernetics. Moscow: Publishing House of Foreign Literature, 829 p. [In Russian].
dc.relation.referencesen[26] Tolbatov, A. (1994). Mathematical Statistics and task optimization algorithms and programs. Kyiv: High School, 226 p. [In Ukrainian].
dc.relation.referencesen[27] Tuluchenko, G. Y. (2008). Geometry computing templates bars of centric averaging method. Bulletin of the Zaporizhzhya National University, 1, 187–190. [In Ukrainian].
dc.relation.referencesen[28] Turchin, V. (2006). Probability and Mathematical Statistics: Concepts, examples, problem. Dnepropetrovsk: Dniprovsky National University, 476 p. [In Ukrainian].
dc.relation.referencesen[29] Vankovych, T.-N. M., Zinko, J. A., & Bozhenko, M. (2010). An averaging method for oscillating stochastic systems with quick phase. Bulletin of the National University "Lviv Polytechnic". Series: Dynamics, Durability and Design of Machines and Devices, 678, 11–14. [In Ukrainian].
dc.relation.referencesen[30] Voronin, A. N. (2004). Method of interconnecting signals for bistatic radar small celestial bodies. System analysis and ma nagement: meas. rep. 9th International. Conf., (pp. 113–114). Moscow: Publishing house of the Moscow Aviation Institute. [In Russian].
dc.relation.referencesen[31] Voronin, A. N. (2006). Synergistic methods of data aggregation. Cybernetics and Systems Analysis, 2, 24–30. [In Russian].
dc.relation.referencesen[32] Voronin, A. N. (2014). Methods of data aggregation. Cybernetics and Systems Analysis, 50(5), 78–84. [In Russian].
dc.relation.referencesen[33] Voronin, A. N., & Ziatdinov, J. K. (2013). Theory and practice of multi-criteria decisions: models, methods, implementation. Saarbrucken (Deutschland); Lambert Academic Publishing, 305 p. [In Russian].
dc.relation.referencesen[34] Voronin, A. N., Ziatdinov, J. K., & Kulinskiy, M. V. (2011). Multicriteria task: models and methods: a monograph. Kyiv: NAU, 348 p. [In Russian].
dc.relation.referencesen[35] Zhluktenko, V. I., & Nakonechny, S. (2000). Probability and Mathematical Statistics: training method. manual. In 2 parts. Part I. Probability. Kyiv: Kyiv National Economic University, 304 p. [In Ukrainian].
dc.relation.referencesen[36] Zhluktenko, V. I., Nakonechny, S., & Savin, S. (2001). Probability and Mathematical Statistics: training method. manual. In 2 parts. Part II. Mathematical Statistics. Kyiv: Kyiv National Economic University, 336 p. [In Ukrainian].
dc.relation.urihttp://nbuv.gov.ua/e-iournals/vntu/2008-4/2008-4.files/uk/08mpbcme.uk.pdf
dc.relation.urihttps://doi.org/10.15421/40250745
dc.relation.urihttps://doi.org/10.15421/40280631
dc.relation.urihttps://doi.org/10.15421/40271025
dc.relation.urihttps://doi.org/10.15421/40290229
dc.relation.urihttps://doi.org/10.15421/40280727
dc.relation.urihttp://jrnl.nau.edu.ua/index.php/IPZ/article/view/3086
dc.relation.urihttp://pidruchniki
dc.rights.holder© Національний університет “Львівська політехніка”, 2019
dc.subjectтеорія ймовірностей
dc.subjectматематична статистика
dc.subjectметоди усереднення даних
dc.subjectінформативний канал передачі даних
dc.subjectмеханізм редукторів ступенів свободи
dc.subjectмеханізм дискримінаторів ступенів свободи
dc.subjectітераційні алгоритми
dc.subjectprobability theory
dc.subjectmathematical statistics
dc.subjectdata averaging methods
dc.subjectinformative data transmission channel
dc.subjectmechanism of reducers of degrees of freedom
dc.subjectthe mechanism of discriminators of degrees of freedom
dc.subjectiterative algorithms
dc.titleRefining expert based evaluation on the basis of a limited quantity of data
dc.title.alternativeУточнення експертних оцінок на підставі обмеженого обсягу даних
dc.typeArticle

Files

Original bundle
Now showing 1 - 2 of 2
No Thumbnail Available
Name:
2019v1n1_Hrytsiuk_Yu_I-Refining_expert_based_58-66.pdf
Size:
542.1 KB
Format:
Adobe Portable Document Format
Download
No Thumbnail Available
Name:
2019v1n1_Hrytsiuk_Yu_I-Refining_expert_based_58-66__COVER.png
Size:
1.85 MB
Format:
Portable Network Graphics
Download
License bundle
Now showing 1 - 1 of 1
No Thumbnail Available
Name:
license.txt
Size:
1.82 KB
Format:
Plain Text
Description:
Download

Collections

Ukrainian Journal of Information Technology. – 2019. – Vol. 1, No. 1