Space Filing Designs for Constrained Domains

Space filling designs are central to studying complex systems, they allow one to understand the overall behaviour of the response over the input space and construct models reduced uncertainty. In many applications a set of constraints are imposed over the inputs that result in a non-rectangular and sometimes non-convex input space. In these cases the existing design construction techniques in the literature cannot be used. We propose a sequential Monte Carlo based algorithm for efficiently generating space filling designs on constrained input spaces. A variant of sequential Monte Carlo sampler is used to generate a large uniform sample over the constrained region. The design is then constructed by sequentially selecting design points from this larger sample with respect to a distance-based design criteria.