Augmenting supersaturated designs with Bayesian D-optimality

A Method for Augmenting Supersaturated Designs with Newly Added Factors

“…Once the data from the first stage have been collected, variable selection methods can be employed to identify active factors and the information from the analysis may be used as a prior to plan the next-stage design. Gutman et al [19] pointed out that the experimenters can classify a factor as a primary term (highlighted by an analysis method or several methods), secondary term (if there is an indication that the term may be active, but it is not predominant), or potential term (with little evidence to suggest it is active). Furthermore, the prior covariance matrix R would be set in terms of the classification.…”

“…where τ 2 < γ 2 . Gutman et al [19] set τ 2 = 5 and γ 2 = 100. Therefore, a Bayesian D-optimal column augmented design (BD-CAD) is created by choosing D 2 to maximize…”

“…Example 1 (CAD for the held-constant factors). Assume that two factors are held-constant and the remaining thirteen factors in Table 1 are planned by a two-level E(s 2 )-optimal SSD(8, 13) presented in Gutman et al [19] in the initial experiment. Table 1 is for the first-stage experiment where the code "0" denotes the specified value for two held-constant factors.…”

“…In general, however, some information would surely have been obtained even if an experiment has failed to achieve the intended goal, and the information gathered should be carefully incorporated to plan the experiment in the next stage. Gutman et al [19] adopted Bayesian D-optimality to add runs to existing SSDs using information from the initial experiment as prior information, and Zhang et al [20] suggested using Bayesian D s -optimality to augment the SSDs. All the above-mentioned studies are merely on row augmented designs.…”

“…The initial designs. Two E(s 2 )-optimal designs, the SSD (8,13) in Table 1 and SSD (7,15) presented in Gutman et al [19], are taken to be the first-stage designs; the latter is shown in Table 5.…”