Bridge Designs for Modeling Systems With Low Noise

For deterministic computer simulations, Gaussian process models are a standard procedure for fitting data. These models can be used only when the study design avoids having replicated points. This characteristic is also desirable for one-dimensional projections of the design, since it may happen that one of the design factors has a strongly nonlinear effect on the response. Latin hypercube designs have uniform one-dimensional projections, but are not efficient for fitting low-order polynomials when there is a small error variance. <i>D</i>-optimal designs are very efficient for polynomial fitting but have substantial replication in projections. We propose a new class of designs that bridge the gap between <i>D</i>-optimal designs and <i>D</i>-optimal Latin hypercube designs. These designs guarantee a minimum distance between points in any one-dimensional projection allowing for the fit of either polynomial or Gaussian process models. Subject to this constraint they are <i>D</i>-optimal for a prespecified model.