Detail publikace

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

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

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"
}