  Space filling designs are central to studying complex systems in various
areas of science. They are used for obtaining an overall understanding of the
behaviour of the response over the input space, model construction and
uncertainty quantification. In many applications a set of constraints are
imposed over the inputs that result in a non-rectangular and sometimes
non-convex input space. Many of the existing design construction techniques in
the literature rely on a set of candidate points on the target space.
Generating a sample on highly constrained regions can be a challenging task. We
propose a sampling algorithm based on sequential Monte Carlo that is
specifically designed to sample uniformly over constrained regions. In
addition, a review of Monte Carlo based design algorithms is provided and the
performance of the sampling algorithm as well as selected design methodology is
illustrated via examples.
