Refining expert based evaluation on the basis of a limited quantity of data
dc.citation.epage | 66 | |
dc.citation.issue | 1 | |
dc.citation.journalTitle | Український журнал інформаційних технологій | |
dc.citation.spage | 58 | |
dc.citation.volume | 1 | |
dc.contributor.affiliation | Національний університет “Львівська політехніка” | |
dc.contributor.affiliation | Lviv Polytechnic National University | |
dc.contributor.author | Грицюк, Юрій Іванович | |
dc.contributor.author | Фернеза, О. Р. | |
dc.contributor.author | Hrytsiuk, Yu. I. | |
dc.contributor.author | Ferneza, O. R. | |
dc.coverage.placename | Львів | |
dc.coverage.placename | Lviv | |
dc.date.accessioned | 2022-05-24T10:02:37Z | |
dc.date.available | 2022-05-24T10:02:37Z | |
dc.date.created | 2019-09-26 | |
dc.date.issued | 2019-09-26 | |
dc.description.abstract | Розроблено 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.abstract | A 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.extent | 58-66 | |
dc.format.pages | 9 | |
dc.identifier.citation | Hrytsiuk 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.citationen | Hrytsiuk 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.uri | https://ena.lpnu.ua/handle/ntb/56875 | |
dc.language.iso | en | |
dc.publisher | Видавництво Львівської політехніки | |
dc.relation.ispartof | Український журнал інформаційних технологій, 1 (1), 2019 | |
dc.relation.ispartof | Ukrainian 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.uri | http://nbuv.gov.ua/e-iournals/vntu/2008-4/2008-4.files/uk/08mpbcme.uk.pdf | |
dc.relation.uri | https://doi.org/10.15421/40250745 | |
dc.relation.uri | https://doi.org/10.15421/40280631 | |
dc.relation.uri | https://doi.org/10.15421/40271025 | |
dc.relation.uri | https://doi.org/10.15421/40290229 | |
dc.relation.uri | https://doi.org/10.15421/40280727 | |
dc.relation.uri | http://jrnl.nau.edu.ua/index.php/IPZ/article/view/3086 | |
dc.relation.uri | http://pidruchniki | |
dc.rights.holder | © Національний університет “Львівська політехніка”, 2019 | |
dc.subject | теорія ймовірностей | |
dc.subject | математична статистика | |
dc.subject | методи усереднення даних | |
dc.subject | інформативний канал передачі даних | |
dc.subject | механізм редукторів ступенів свободи | |
dc.subject | механізм дискримінаторів ступенів свободи | |
dc.subject | ітераційні алгоритми | |
dc.subject | probability theory | |
dc.subject | mathematical statistics | |
dc.subject | data averaging methods | |
dc.subject | informative data transmission channel | |
dc.subject | mechanism of reducers of degrees of freedom | |
dc.subject | the mechanism of discriminators of degrees of freedom | |
dc.subject | iterative algorithms | |
dc.title | Refining expert based evaluation on the basis of a limited quantity of data | |
dc.title.alternative | Уточнення експертних оцінок на підставі обмеженого обсягу даних | |
dc.type | Article |
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