Joint Research Conference
June 24-26, 2014
Computer models are used to explore the response in physical systems and are often used in place of, or in addition to, experiments on the process. The experiment design plays a crucial role in the success of the virtual experiment. In this work a novel type of space-filling design is proposed that is based on a type of sampling lattice that contains rotated and scaled versions of themselves (these are not Cartesian lattices). The designs have the property that the Vornoi regions around each design point have the same volume – a type space-filling property. A sequence of designs is completely described by a lattice basis, an integer (dilation) matrix, and a shift of origin. To construct experimental designs of any desired run-size in a bounded region of interest, we optimize shift and rotation of the initial lattice. A key feature of our construction is that further run-sizes that result from refining or coarsening the initial grid can be chosen to vary by any integer factor as low as 2. The proposed approach is flexible insofar as it can be used to optimize additional space-filling criteria, such as the packing diameter (minimum inter-point distance), which is known to impose a bound on the integrated mean square prediction error in Gaussian process regression. This is joint work with Steven Bergner (SFU) and Torsten Moller (University of Vienna).