Improved formulation of MaxiMin Criterion for Space-Filling Designs

Kód výsledku v 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>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Improved formulation of MaxiMin Criterion for Space-Filling Designs

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Improved formulation of MaxiMin Criterion for Space-Filling Designs

Popis výsledku anglicky

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.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

20101 - Civil engineering

Projekt

<a href="/cs/project/GA16-22230S" target="_blank" >GA16-22230S: Rozvoj pokročilých simulačních metod pro statistickou analýzu konstrukcí</a><br>

Návaznosti

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

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název statě ve sborníku

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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Počet stran výsledku

10

Strana od-do

1697-1706

Název nakladatele

TU-Verlag Vienna,

Místo vydání

Vienna, Austria

Místo konání akce

Vienna

Datum konání akce

6. 8. 2017

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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