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

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

WoS Article

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.

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.

Design of experiments for computer models; Latin hypercube sampling; Periodic metric; Space-filling designs; Uniform design; Variance reduction

Design of experiments for computer models; Latin hypercube sampling; Periodic metric; Space-filling designs; Uniform design; Variance reduction

VOŘECHOVSKÝ, M.; ELIÁŠ, J.

2021

28.07.2020

AMER STATISTICAL ASSOC

ALEXANDRIA

1537-2723

TECHNOMETRICS

62

3

United States of America

371

386

16

https://www.tandfonline.com/doi/full/10.1080/00401706.2019.1639550

46j
159828-Article
159828-Modification-Vorechovsky-přínos k poznání 2024