A Sphericity Filter for Space-Filling Designs in Nondeterministic Experiments

Abstract

Space-filling designs support flexible modeling in noisy multi-response experiments, but an individual design can give poor precision for low-order effects. We use a low-order working model to identify effects whose estimation precision we seek to protect, while allowing a more complex final response model. The filter selects one complete design from a candidate pool by minimizing a geometric loss divided by sphericity, without exchanging or altering its points. Sphericity measures the balance of the working-model confidence ellipsoid's principal-axis variances, independently of its volume. In a working-model basis orthonormal over the prediction region, sphericity is the shape factor of the I-criterion, which measures average prediction variance. In cube studies with quadratic least-squares and Gaussian-process fits, this target filter gives modest average prediction gains over the geometrically best candidate at small geometric cost. Gains in working-model precision are largest near saturation: in a four-factor example, worst-decile prediction standard error falls by about a quarter relative to the geometrically best candidate. In constrained mixtures, raw coefficient-based filtering and A-optimality can emphasize extrapolated Scheffe coefficients and yield poor regional prediction precision. Target filtering improves regional working-model precision in most settings studied, mirroring the advantage of I- over A-optimality for highly constrained mixture designs.

arXiv comment30 pages: 20-page main article with 5 figures and 5 numbered tables, followed by a 10-page supplement with 2 figures and 9 numbered tables