Sliced rotated sphere packing designs

Space-filling designs are popular choices for computer experiments. A sliced design is a design that can be partitioned into several subdesigns. We propose a new type of sliced space-filling design called sliced rotated sphere packing designs. Their full designs and subdesigns are rotated sphere packing designs. They are constructed by rescaling, rotating, translating and extracting the points from a sliced lattice. We provide two fast algorithms to generate such designs. Furthermore, we propose a strategy to use sliced rotated sphere packing designs adaptively. Under this strategy, initial runs are uniformly distributed in the design space, follow-up runs are added by incorporating information gained from initial runs, and the combined design is space-filling for any local region. Examples are given to illustrate its potential application

On existence and construction of balanced arrays

AbstractThis paper surveys existence conditions and construction procedures for balanced arrays. A necessary and sufficient condition for the existence of an s-symbol balanced array of strength t with m constraints is discussed. The construction of an s-symbol balanced array of strength 2, based on an (r, λ)-design with mutually balanced nested subdesigns, is presented. Related open problems are exhibited

Resolvable designs with large blocks

Resolvable designs with two blocks per replicate are studied from an optimality perspective. Because in practice the number of replicates is typically less than the number of treatments, arguments can be based on the dual of the information matrix and consequently given in terms of block concurrences. Equalizing block concurrences for given block sizes is often, but not always, the best strategy. Sufficient conditions are established for various strong optimalities and a detailed study of E-optimality is offered, including a characterization of the E-optimal class. Optimal designs are found to correspond to balanced arrays and an affine-like generalization.Comment: Published at http://dx.doi.org/10.1214/009053606000001253 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org