Periodic version of the minimax distance criterion for Monte Carlo integration
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26110%2F20%3APU137297" target="_blank" >RIV/00216305:26110/20:PU137297 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0965997820300508" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0965997820300508</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.advengsoft.2020.102900" target="_blank" >10.1016/j.advengsoft.2020.102900</a>
Alternative languages
Result language
angličtina
Original language name
Periodic version of the minimax distance criterion for Monte Carlo integration
Original language description
The selection of points for numerical integration of the Monte Carlo type, largely used in analysis of engineering problems, is developed. It is achieved by modification of the metric in the minimax optimality criterion. The standard minimax criterion ensures the design exhibits good space-filling property and therefore reduces the variance of the estimator of the integral. We, however, show that the points are not selected with the same probability over the space of sampling probabilities: some regions are over- or under-sampled when designs are generated repetitively. This violation of statistical uniformity may lead to systematically biased integral estimators. We propose that periodic metric be considered for calculation of the minimax distance. Such periodic minimax criterion provides statistically uniform designs leading to unbiased integration results and also low estimator variance due to retained space-filling property. These conclusions are demonstrated by examples integrating analytical functions. The designs are constructed by two different algorithms: (i) a new time-stepping algorithm resembling a damped system of attracted particles developed here, and (ii) the heuristic swapping of coordinates. The designs constructed by the time-stepping algorithm are attached to the paper as a supplementary material. The computer code for construction of the designs is attached too.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
20101 - Civil engineering
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
ADVANCES IN ENGINEERING SOFTWARE
ISSN
0965-9978
e-ISSN
1873-5339
Volume of the periodical
149
Issue of the periodical within the volume
1
Country of publishing house
GB - UNITED KINGDOM
Number of pages
13
Pages from-to
1-13
UT code for WoS article
000577084300007
EID of the result in the Scopus database
2-s2.0-85090854333