LatticeDesign-package {LatticeDesign}

LatticeDesign package

Description

Generate lattice-based space-filling designs with fill or separation distance properties. These include interleaved lattice-based minimax distance designs, interleaved lattice-based maximin distance designs, (sliced) rotated sphere packing designs, and densest packing-based maximum projections designs.

Details

Package:	LatticeDesign
Type:	Package
Version:	2.0-4
Date:	2020-12-4
License:	LGPL-2.1

Important functions in this package are: InterleavedMinimaxD generates an interleaved lattice-based minimax distance design. InterleavedMaximinD generates an interleaved lattice-based maximin distance design. DPMPD generates a densest packing-based maximum projection design. RSPD generates a rotated sphere packing design. SlicedRSPD generates a sliced rotated sphere packing design by partitioning one rotated sphere packing design. AdaptiveRSPD generates a sliced rotated sphere packing design by enlarging one rotated sphere packing design.

All those functions generate space-filling designs with fill or separation distance properties. Such designs are useful for accurate emulation of computer experiments, fitting nonparametric models and resource allocation. They are constructed from lattices, i.e., sets of points with group structures.

RSPD and DPMPD generate designs in two to eight dimensions with both unprojected and projective distance properties. Such designs are desirable when possibly the output value is insensitive to some variables. DPMPD can be seen as an upgrade of RSPD using new magic rotation matrices. Another distinction is that RSPD generates designs with better unprojected fill distance for nonboundary regions while DPMPD generates designs with better unprojected separation distance. RSPD and DPMPD construct designs by rescaling, rotating, translating and extracting the points of the lattice with asymptotically optimal fill and separation distance, respectively.

SlicedRSPD and AdaptiveRSPD generate sliced rotated sphere packing designs, i.e., a rotated sphere packing design that can be partitioned into several smaller rotated sphere packing designs. SlicedRSPD partitions one rotated sphere packing design. The generated designs are useful for computer experiments with a categorical variable, computer experiments from multiply resources and model validation. Alternatively, AdaptiveRSPD enlarges a smaller rotated sphere packing design, which is useful for adaptive design of computer experiments.

InterleavedMinimaxD generates designs in two to eight dimensions with low fill distance. InterleavedMaximinD generates designs with high separation distance. InterleavedMaximinD allows users to specify the relative importance of variables and is applicable to problems with any number of variables. Such designs are useful for accurate emulation of computer experiments when the variables are almost equally important in predicting the output value or relatively accurate a priori guess on the variable importance is available. On the other hand, such designs are poor in projective distance properties and are thus not recommended when the output value is insensitive to many unknown variables.

Author(s)

Maintainer: Xu He <[e-mail]>

References

He, Xu (2017). "Rotated sphere packing designs", Journal of the American Statistical Association, 112(520): 1612-1622.

He, Xu (2017). "Interleaved lattice-based minimax distance designs", Biometrika, 104(3): 713-725.

He, Xu (2018). "Lattice-based designs with quasi-uniform projections", arXiv:1709.02062v2.

He, Xu (2019). "Interleaved lattice-based maximin distance designs", Biometrika, 106(2): 453-464.

He, Xu (2019). "Sliced rotated sphere packing designs", Technometrics, 61(1): 66-76.

He, Xu (2020). "Lattice-based designs possessing quasi-optimal separation distance on all projections", Biometrika, accepted, DOI:10.1093/biomet/asaa057.