A1969
Title: Approximate mixture designs under the DuMouchel-Jones Bayesian D-optimality criterion
Authors: Hsiang-Ling Hsu - National University of Kaohsiung (Taiwan) [presenting]
Abstract: Optimal designs for mixture experiments are typically constructed under a specified regression model, but their performance can be sensitive to model misspecification or omitted terms. A Bayesian modification of D-optimality is employed to distinguish primary inferential terms from potential terms representing possible model expansion. Approximate designs for Scheffe quadratic mixture models are investigated on a continuous simplex under this Bayesian criterion. An equivalence theorem is established to characterize optimality and to verify candidate designs. For three- and four-component mixtures, the optimal supports are shown to concentrate on geometrically interpretable boundary points, specifically simplex vertices and edge midpoints. The associated design weights vary systematically with the prior adjustment parameter, reflecting the balance between the primary model and potential expansions. Numerical investigations for five- and six-component mixtures suggest that these structural patterns persist in higher-dimensional mixture spaces. Existing discrete designs are evaluated using D-efficiency under the same criterion, and computational verification is supported by particle swarm optimization and an interactive Shiny application. The resulting framework supports robustified approximate designs for mixture experiments under model uncertainty.
