Input-response space-filling designs incorporating response uncertainty

Traditionally space-filling designs have focused on the characteristics of the design in the input space ensuring uniform spread throughout the region. Input-response space-filling designs considered scenarios when having good spread throughout the range or region of the responses is also of interest. This paper acknowledges that there is typically uncertainty associated with the values of the response(s) and hence proposes a method, Input-Response Space-Filling Designs with Uncertainty (IRSFwU), to incorporate this into the design construction. The Pareto front of designs offers alternatives that balance input and response space filling, while prioritizing input combinations with lower associated response uncertainty. These lower uncertainty choices improve the chances of observing the desired response values. We describe the new approach with an uncertainty-adjusted distance to measure the response space filling, the Pareto aggregate point exchange algorithm to populate the set of promising designs, and illustrate the method with three examples of different input and response relationships and dimensions.