Unrestricted Bridge (U‐Bridge) Designs for Settings with Non‐deterministic Data

ABSTRACT We propose a simple method to generate designs for continuous factors when the response data are noisy. Our “unrestricted bridge (U‐bridge) designs” are closely related to the bridge designs of Jones et al., but are much easier to construct. Like those designs, the U‐bridge designs provide a middle ground between optimal designs and traditional space‐filling designs. A compromise between the design approaches has several advantages. It supports fitting both the polynomial models that typically drive optimal designs and more flexible models, like Gaussian process regression, which work best when design points are more spread out. It enables the user to place more or less emphasis on controlling variance and bias. When data are noisy, as we assume here, it is important to keep variance in mind in the experimental plan. Purely space‐filling designs, which were inspired for use with deterministic simulators, are entirely focused on bias reduction, completely ignoring variance. This becomes increasingly problematic as the level of noise increases. Optimal designs are geared entirely toward variance for a designated approximating model, completely ignoring the bias that results from the fact that the model is only intended as a good approximation. Our U‐bridge designs provide protection from both variance and bias.