Improved formulation of MaxiMin Criterion for Space-Filling Designs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26110%2F17%3APU127190" target="_blank" >RIV/00216305:26110/17:PU127190 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Improved formulation of MaxiMin Criterion for Space-Filling Designs
Original language description
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.
Czech name
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Czech description
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Project
<a href="/en/project/GA16-22230S" target="_blank" >GA16-22230S: Development of advanced sampling methods for statistical analysis of structures</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
Safety, Reliability, Risk, Resilience and Sustainability of Structures and Infrastructure
ISBN
978-3-903024-28-1
ISSN
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e-ISSN
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Number of pages
10
Pages from-to
1697-1706
Publisher name
TU-Verlag Vienna,
Place of publication
Vienna, Austria
Event location
Vienna
Event date
Aug 6, 2017
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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