Stochastical computation methods and experimental designing
DOI:
https://doi.org/10.21638/spbu01.2023.201Abstract
This paper contains a brief review of the most important results obtained by the staff of the department of statistical modeling. Results include mathematical justification of computer simulation of randomness, stochastic methods of solving equations, stochastic optimization, study of stochastic stability and parallelism of Monte-Carlo algorithms. In the area of experiment planning, special attention is paid to regression experiment under nonlinear parameterization. The list of references mainly includes monographs written by members of the department. The exceptions are some articles with results not included in them.Keywords:
stochastic modeling, Monte-Carlo method, pseudorandom numbers, Markov chains, stochastic optimization, regression experiment, optimal experiment design, regression models nonlinear in parameters, functional approach, hyper exponential models, fractionally rational models, locally optimal experimental designs
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References
Литература
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2. Ермаков С. М. Метод Монте-Карло и смежные вопросы. Москва, Наука (1975).
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6. Nekrutkin V. V., Samachova M. Admissidle and аsymptotically optimal linear congruential generators. Monte-Carlo methods and applications 13 (3), 27-44 (2007).
7. Franclin J. N. Deterministic simulation of random processes. Math. Comp. 17, 28-59 (1963).
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20. Ermakov S. M., Leora S. N. Decrease of the mean of the quasi-random integration error. Communications in Statistics: Simulation and Computation 50, iss. 11, 3581-3589 (2021).
21. Ермаков С. М., Рукавишникова А. И., Тимофеев К. А. О некоторых стохастических и квазистохастических методах решения уравнений. Вестник Санкт-Петербургского университета. Математика. Механика. Астрономия 4 (1), 75-83 (2008).
22. Ermakov S. M., Melas V. B. Design and Analysis simulation Experiments. Dortrecht; Boston; London, Kluver Academic Publisher (1993).
23. Melas V. B. Functional Approach to Optimal Experimental Design. New York, Springer-Verlag (2006).
24. Мелас В. Б., Шпилев П. В. L-оптимальные планы для регрессионноймодели Фурье без свободного члена. Вестник Санкт-Петербургского университета. Математика. Механика. Астрономия 9 (67), вып. 1, 64-75 (2022). https://doi.org/10.21638/spbu01.2022.107
25. Melas V. B., Guchenko R., Strashko V. Standardized maximin criterion for discrimination and parameter estimation of nested models. Communications in Statistics-Simulation and а Computation 51 (8), 4314-4325 (2022).
26. Dette H., Melas V. B., Shpilev P. V. A note on optimal designs for estimating the slope of a polynomial regression. Statistics and Probability Letters 170, 108992 (2021)
27. Dette H., Melas V. B., Shpilev P. V. Some explicit solutions of c-optimal design problems for polynomial regression with no intercept. Annals of the Institute of Statistical Mathematics 73 (1), 61-82 (2021).
28. Мелас В. Б., Шпилев П. В. Построение c-оптимальных планов для полиномиальнойрегрессии без свободного члена. Вестник Санкт-Петербургского университета. Математика. Механика. Астрономия 7 (65), вып. 2, 331-342 (2020). https://doi.org/10.21638/11701/spbu01.2020.215
References
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4. Ermakov S. M. Monte-Carlo in computational mathematic. Introductory course. Moscow, Binom Publ. (2009). (In Russian)
5. Nekrutkin V. V. On the complexity of binary floating point pseudorandom generator. Monte-Carlo methods and applications 22 (2), 109-111 (2016).
6. Nekrutkin V. V., Samachova M. Admissidle and аsymptotically optimal linear congruential generators. Monte-Carlo methods and applications 13 (3), 27-44 (2007).
7. Franclin J. N. Deterministic simulation of random processes. Math. Comp. 17, 28-59 (1963).
8. Ermakov S. M., Sipin A. S. Monte-Carlo Method and parametrically separable algorithms. St Petersburg, St Рetersburg University Press (2014). (In Russian)
9. Ermakov S. M., Wagner W. Monte-Carlo difference schemes for the wave equations. Monte-Carlo methods and applications 8 (1), 1-29 (2002).
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15. Ermakov S. M., Surovikina T. O. Backward iterations for solving integral equations with polynomial nonlinearity. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 9 (67), iss. 1, 23-36. (2022). https://doi.org/10.21638/spbu01.2022.103 [Eng. transl.: Vestnik St Petersburg University. Mathematics 55, iss. 1, 16-26 (2022). https://doi.org/10.1134/S1063454122010046].
16. Ermakov S. M., Smilovitskiy M. G. Monte-Carlo for solving large linear systems ofordinary differential equations. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 8 (66), iss. 1, 37-48 (2021). https://doi.org/10.21638/spbu01.2021.104 (In Russian) [Eng. transl.: Vestnik St Petersburg University. Mathematics 54, iss. 1, 28-38 (2021). https://doi.org/10.1134/S106345412101].
17. Ermakov S. M.,Tovstik T. M. Monte-Carlo method for solution of systems ODE. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 6 (64), iss. 3, 411-421 (2019). https://doi.org/10.21638/11701/spbu01.2019.306 (In Russian) [Eng. transl.: Vestnik St Petersburg University. Mathematics 52, iss. 3, 272-280 (2019). https://doi.org/10.1134/S1063454119030087].
18. Ermakov S. M. Kashtanov J. N. (eds) Monte-Carlo method in financional mathematics. St Petersburg, St Рetersburg University Press (2006). (In Russian)
19. Kulikov D. V., Leora S. N., Ermakov S. M. Towards the Analysis of the simulated annealing method in the multiextremal case. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 4 (62), iss. 2, 220-226 (2017). https://doi.org/10.21638/11701/spbu01.2017.205 (In Russian) [Eng. transl.: Vestnik St Petersburg University. Mathematics 50, iss. 2, 132-137 (2017)].
20. Ermakov S. M., Leora S. N. Decrease of the mean of the quasi-random integration error. Communications in Statistics: Simulation and Computation 50, iss. 11, 3581-3589 (2021).
21. Ermakov S. M., Rukavichnikova A. I., Timofeev K. A. On some stochastic and quasistochastic methods for equanion solving. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 4 (1), 75-83. (2008). (In Russian) [Eng. transl.: Vestnik St Petersburg University. Mathematics 41, 348-354 (2008). https://doi.org/10.3103/S1063454108040109].
22. Ermakov S. M., Melas V. B. Design and Analysis simulation Experiments. Dortrecht; Boston; London, Kluver Academic Publisher (1993).
23. Melas V. B. Functional Approach to Optimal Experimental Design. New York, Springer-Verlag (2006).
24. Melas V. B., Shpilev P. V. L-optimal designs for a trigonometric Fourier regression model with no intercept. Vestnik of Saint Petersburg University. Mathematics. Mechanics.Astronomy 9 (67), iss. 1, 64-75 (2022). https://doi.org/10.21638/spbu01.2022.107 (In Russian) [Eng. transl.: Vestnik St Petersburg University. Mathematics 55, iss. 1, 48-56 (2022). https://doi.org/10.1134/S1063454122010095].
25. Melas V. B., Guchenko R., Strashko V. Standardized maximin criterion for discrimination and parameter estimation of nested models. Communications in Statistics-Simulation and а Computation 51 (8), 4314-4325 (2022).
26. Dette H., Melas V. B., Shpilev P. V. A note on optimal designs for estimating the slope of a polynomial regression. Statistics and Probability Letters 170, 108992 (2021)
27. Dette H., Melas V. B., Shpilev P. V. Some explicit solutions of c-optimal design problems for polynomial regression with no intercept. Annals of the Institute of Statistical Mathematics 73 (1), 61-82 (2021).
28. Melas V. B., Shpilev P. V. Constructing c-optimal designs for polynomial regression without an intercept. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 7 (65), iss. 2, 331-342 (2020). https://doi.org/10.21638/11701/spbu01.2020.215 (In Russian) [Eng. transl.: Vestnik St Petersburg University. Mathematics 53, iss. 2, 223-231 (2020). https://doi.org/10.1134/S1063454120020120].
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Published
2023-05-10
How to Cite
Ermakov, S. M., & Melas, V. B. (2023). Stochastical computation methods and experimental designing. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 10(2), 187–199. https://doi.org/10.21638/spbu01.2023.201
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Mathematics
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Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.
