Corpus ID: 88522082

Four-Point, 2D, Free-Ranging, IMSPE-Optimal, Twin-Point Designs

@article{Crary2015FourPoint2F,
  title={Four-Point, 2D, Free-Ranging, IMSPE-Optimal, Twin-Point Designs},
  author={S. Crary and J. Stormann},
  journal={arXiv: Methodology},
  year={2015}
}
We report the discovery of a set of four-point, two-factor, free-ranging, putatively IMSPE-optimal designs with a pair of twin points, in the statistical design of computer experiments, under Gaussian-process, fixed-Gaussian-covariance parameter, and zero-nugget assumptions. We conjecture this is the set of free-ranging, twin-point designs with the smallest number of degrees of freedom. 
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References

SHOWING 1-9 OF 9 REFERENCES
Spatial sampling design for parameter estimation of the covariance function
We study the spatial optimal sampling design for covariance parameter estimation. The spatial process is modeled as a Gaussian random field and maximum likelihood (ML) is used to estimate theExpand
Accurate emulators for large-scale computer experiments
Large-scale computer experiments are becoming increasingly important in science. A multi-step procedure is introduced to statisticians for modeling such experiments, which builds an accurateExpand
Spatial sampling design under the infill asymptotic framework
We study optimal sample designs for prediction with estimated parameters. Recent advances in the infill asymptotic theory provide a deeper understanding of the finite sample behavior of predictionExpand
Fast Prediction of Deterministic Functions Using Sparse Grid Experimental Designs
TLDR
It is demonstrated that when a general set of designs is employed, the resulting predictor is quick to compute and has reasonable accuracy, and some empirical comparisons to the more common space-filling designs are details that verify the designs are competitive in terms of resulting prediction accuracy. Expand
Optimal designs for variogram estimation
The variogram plays a central role in the analysis of geostatistical data. A valid variogram model is selected and the parameters of that model are estimated before kriging (spatial prediction) isExpand
Statistical design and analysis of computer experiments for the generation of parsimonious metamodels
  • S. Crary
  • Engineering
  • Symposium on Design, Test, Integration, and Packaging of MEMS/MOEMS
  • 2001
We review the use of statistical design and analysis of computer experiments (DACE) for the generation of parsimonious, surrogate models, also known as metamodels. Such metamodels are used to replaceExpand
Design of Computer Experiments for Metamodel Generation
TLDR
This work reviews the use of statistical design and analysis of computer experiments (DACE) for the generation of parsimonious, surrogate models, also known as metamodels, to replace cpu- or memory-intensive, discretized approximations that often arise in MEMS and MOEMS. Expand
The Design and Analysis of Computer Experiments
Optimal predictive designs for experiments that involve computer simulators