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Article information
2016 , Volume 21, ¹ 2, p.42-52
Semenov K.K.
The reliability of Monte-Carlo approach for applications in the interval analysis problems
Purpose. One of the major problems in interval analysis is to estimate the function of limit values, which is achievable within the specified range of possible values of its arguments. To solve this problem, we use different methods that include statistical modelling. In the latter case, final boundaries will be always narrower than the range of values of the exact function. As it is mentioned in literature, this indicated that the methods of statistical modelling do not provide results with the guaranteed reliability, since the interval that contains actually all possible values of the studied function may be essentially wider than the boundaries obtained from the statistical modelling. The goal of this paper is to derive the statistical estimate for the reliability of the results of Monte-Carlo approach for interval analysis. Methodology. To study the reliability, we use the tools of the probability theory. The estimate for the function range can be considered as reliable if the probability of statement “the interval obtained using the Monte Carlo method, contains more than a specified proportion of all possible values of a function” is very close to one. All necessary proofs are given showing that the derived relations are correct for all possible functions involved in the interval analysis and for all distributions used in Monte-Carlo approach. Findings. The derived relations connect reliability characteristics with quantity of statistical tests. Easy to use approximations of these relations are presented. It is shown how to estimate the sufficient quantity of statistical tests that will provide the necessary reliability for Monte-Carlo estimates for possible range of studied function and how to calculate the guaranteed confidence for the quantity of the given tests. Originality/value. All results presented in the paper are original. The presented relations allow to get quantitative estimate for quality of the results of interval analysis obtained with Monte-Carlo method and to reasonably choose the quantity of statistical tests, which are required to execute.
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Keywords: Monte-Carlo method, interval analysis, statistical tests quantity
Author(s):
Semenov Konstantin Konstantinovich
PhD. , Associate Professor
Position: Leading research officer
Office: St. Petersburg Polytechnic University, 23 State Marine Design Institute Branch of 31 State Design Institute of Special Construction
Address: 195251, Russia, St-Petersburg, 29, Polytechnicheskaya str.
Phone Office: (812) 297-60-01
E-mail: semenov.k.k@gmail.com
SPIN-code: 5527-1193 References:
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Bibliography link:
Semenov K.K. The reliability of Monte-Carlo approach for applications in the interval analysis problems // Computational technologies. 2016. V. 21. ¹ 2. P. 42-52
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