Publication detail

Periodic version of the minimax distance criterion for Monte Carlo integration

ELIÁŠ, J. VOŘECHOVSKÝ, M. SADÍLEK, V.

Original Title

Periodic version of the minimax distance criterion for Monte Carlo integration

Type

journal article in Web of Science

Language

English

Original Abstract

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.

Keywords

Numerical integration; Design of experiments; Space-filling designs; Latin hypercube sampling; Voronoï tessellation; Periodic space

Authors

ELIÁŠ, J.; VOŘECHOVSKÝ, M.; SADÍLEK, V.

Released

1. 11. 2020

Publisher

Elsevier

ISBN

0965-9978

Periodical

ADVANCES IN ENGINEERING SOFTWARE

Year of study

149

Number

1

State

United Kingdom of Great Britain and Northern Ireland

Pages from

1

Pages to

13

Pages count

13

URL

https://www.sciencedirect.com/science/article/pii/S0965997820300508

Full text in the Digital Library

http://hdl.handle.net/11012/196691

BibTex

@article{BUT165338,
  author="Jan {Eliáš} and Miroslav {Vořechovský} and Václav {Sadílek}",
  title="Periodic version of the minimax distance criterion for Monte Carlo integration",
  journal="ADVANCES IN ENGINEERING SOFTWARE",
  year="2020",
  volume="149",
  number="1",
  pages="1--13",
  doi="10.1016/j.advengsoft.2020.102900",
  issn="0965-9978",
  url="https://www.sciencedirect.com/science/article/pii/S0965997820300508"
}