Publication detail

Improved formulation of MaxiMin Criterion for Space-Filling Designs

ELIÁŠ, J. VOŘECHOVSKÝ, M.

Original Title

Improved formulation of MaxiMin Criterion for Space-Filling Designs

Type

conference paper

Language

English

Original Abstract

The MaxiMin criterion was developed to achieve optimal distribution of experimental points in a design domain. For simplicity, we consider the design domain to be a unit hypercube. Some authors consider the MaxiMin criterion to prefer point layouts that are space-filling and uniform. In this paper we show that the MaxiMin criterion provides strongly nonuniform designs due to the effect of the boundaries of the hypercube within which the distances are measured. The nonuniformity is a serious problem when applying the designs for Monte Carlo integration. We propose a simple remedy to the MaxiMin criterion that lies in the assumption of periodic boundary conditions. The biased behavior of the original MaxiMin (Mm) criterion and excellent performance of the modified criterion (PMm) are demonstrated using simple numerical examples focused on (i) the uniformity of sampling density over the design space and, (ii) statistical sampling efficiency measured through the ability to correctly estimate the statistical parameters of functions of random variables.

Keywords

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Authors

ELIÁŠ, J.; VOŘECHOVSKÝ, M.

Released

6. 10. 2017

Publisher

TU-Verlag Vienna,

Location

Vienna, Austria

ISBN

978-3-903024-28-1

Book

Safety, Reliability, Risk, Resilience and Sustainability of Structures and Infrastructure

Pages from

1697

Pages to

1706

Pages count

10

BibTex

@inproceedings{BUT146115,
  author="Jan {Eliáš} and Miroslav {Vořechovský}",
  title="Improved formulation of MaxiMin Criterion for Space-Filling Designs",
  booktitle="Safety, Reliability, Risk, Resilience and Sustainability of Structures and Infrastructure",
  year="2017",
  pages="1697--1706",
  publisher="TU-Verlag Vienna,",
  address="Vienna, Austria",
  isbn="978-3-903024-28-1"
}