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VOŘECHOVSKÝ, M. ELIÁŠ, J.
Originální název
Modification of the Maximin and phi(p) (Phi) Criteria to Achieve Statistically Uniform Distribution of Sampling Points
Typ
článek v časopise ve Web of Science, Jimp
Jazyk
angličtina
Originální abstrakt
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.
Klíčová slova
Design of experiments for computer models; Latin hypercube sampling; Periodic metric; Space-filling designs; Uniform design; Variance reduction
Autoři
VOŘECHOVSKÝ, M.; ELIÁŠ, J.
Vydáno
28. 7. 2020
Nakladatel
AMER STATISTICAL ASSOC
Místo
ALEXANDRIA
ISSN
1537-2723
Periodikum
Technometrics
Ročník
62
Číslo
3
Stát
Spojené státy americké
Strany od
371
Strany do
386
Strany počet
16
URL
https://www.tandfonline.com/doi/full/10.1080/00401706.2019.1639550
BibTex
@article{BUT159828, author="Miroslav {Vořechovský} and Jan {Eliáš}", title="Modification of the Maximin and phi(p) (Phi) Criteria to Achieve Statistically Uniform Distribution of Sampling Points", journal="Technometrics", year="2020", volume="62", number="3", pages="371--386", doi="10.1080/00401706.2019.1639550", issn="1537-2723", url="https://www.tandfonline.com/doi/full/10.1080/00401706.2019.1639550" }