Bridge designs for modeling systems with low noise

Bradley Jones, Rachel T. Silvestrini, Douglas Montgomery, David M. Steinberg

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

For deterministic computer simulations, Gaussian process models are a standard procedure for fitting data. These models can be used only when the study design avoids having replicated points. This characteristic is also desirable for one-dimensional projections of the design, since it may happen that one of the design factors has a strongly nonlinear effect on the response. Latin hypercube designs have uniform one-dimensional projections, but are not efficient for fitting low-order polynomials when there is a small error variance. D-optimal designs are very efficient for polynomial fitting but have substantial replication in projections. We propose a new class of designs that bridge the gap between D-optimal designs and D-optimal Latin hypercube designs. These designs guarantee a minimum distance between points in any one-dimensional projection allowing for the fit of either polynomial or Gaussian process models. Subject to this constraint they are D-optimal for a prespecified model.

Original languageEnglish (US)
Pages (from-to)155-163
Number of pages9
JournalTechnometrics
Volume57
Issue number2
DOIs
StatePublished - Apr 3 2015

Fingerprint

System Modeling
D-optimal Design
Latin Hypercube Design
Projection
Gaussian Model
Gaussian Process
Process Model
Polynomial
D-optimal
Data Fitting
Polynomials
Nonlinear Effects
Minimum Distance
Replication
Computer Simulation
Design
Model
Computer simulation

Keywords

  • Computer experiments
  • Gaussian process model
  • Optimal design
  • Space-filling designs

ASJC Scopus subject areas

  • Modeling and Simulation
  • Statistics and Probability
  • Applied Mathematics

Cite this

Bridge designs for modeling systems with low noise. / Jones, Bradley; Silvestrini, Rachel T.; Montgomery, Douglas; Steinberg, David M.

In: Technometrics, Vol. 57, No. 2, 03.04.2015, p. 155-163.

Research output: Contribution to journalArticle

Jones, B, Silvestrini, RT, Montgomery, D & Steinberg, DM 2015, 'Bridge designs for modeling systems with low noise', Technometrics, vol. 57, no. 2, pp. 155-163. https://doi.org/10.1080/00401706.2014.923788
Jones, Bradley ; Silvestrini, Rachel T. ; Montgomery, Douglas ; Steinberg, David M. / Bridge designs for modeling systems with low noise. In: Technometrics. 2015 ; Vol. 57, No. 2. pp. 155-163.
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