Periodic version of the minimax distance criterion for Monte Carlo integration

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Periodic version of the minimax distance criterion for Monte Carlo integration

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Periodic version of the minimax distance criterion for Monte Carlo integration

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

20101 - Civil engineering

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

ADVANCES IN ENGINEERING SOFTWARE

ISSN

0965-9978

e-ISSN

1873-5339

Svazek periodika

149

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

13

Strana od-do

1-13

Kód UT WoS článku

000577084300007

EID výsledku v databázi Scopus

2-s2.0-85090854333