Modification of the Maximin and phi(p) (Phi) Criteria to Achieve Statistically Uniform Distribution of Sampling Points

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26110%2F20%3APU134111" target="_blank" >RIV/00216305:26110/20:PU134111 - isvavai.cz</a>

Result on the web

<a href="https://www.tandfonline.com/doi/full/10.1080/00401706.2019.1639550" target="_blank" >https://www.tandfonline.com/doi/full/10.1080/00401706.2019.1639550</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1080/00401706.2019.1639550" target="_blank" >10.1080/00401706.2019.1639550</a>

Result language

angličtina

Original language name

Modification of the Maximin and phi(p) (Phi) Criteria to Achieve Statistically Uniform Distribution of Sampling Points

Original language description

This article proposes a sampling technique that delivers robust designs, that is, point sets selected from a design domain in the shape of a unit hypercube. The designs are guaranteed to provide a statistically uniform point distribution, meaning that every location has the same probability of being selected. Moreover, the designs are sample uniform, meaning that each individual design has its points spread evenly throughout the domain. The sample uniformity (often measured via a discrepancy criterion) is achieved using distance-based criteria ( or Maximin), that is, criteria normally used in space-filling designs. We show that the standard intersite metrics employed in distance-based criteria (Maximin and (phi)) do not deliver statistically uniform designs. Similarly, designs optimized via centered L-2 discrepancy or support points are also not statistically uniform. When these designs (after optimization based on intersite distances) are used for Monte Carlo type of integration, their statistical nonuniformity is a serious problem as it may lead to a systematic bias. This article proposes using a periodic metric to guarantee the statistical uniformity of the family of distance-based designs. The presented designs used as benchmarks in the article are only taken from the class of Latin hypercube designs, which forces univariate projections to be uniform and improves accuracy in Monte Carlo integration of some functions. for this article are available online.

Czech name

—

Czech description

—

Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10103 - Statistics and probability

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

2020

Confidentiality

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

Name of the periodical

Technometrics

ISSN

0040-1706

e-ISSN

1537-2723

Volume of the periodical

62

Issue of the periodical within the volume

3

Country of publishing house

US - UNITED STATES

Number of pages

16

Pages from-to

371-386

UT code for WoS article

000484398500001

EID of the result in the Scopus database

2-s2.0-85071304878