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Abstract:
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Much of the literature on the design and analysis of supersaturated designs (SSDs), in which the number of factors exceeds the number of runs, rests on design principles assuming a least-squares analysis. More recently, researchers have discovered the potential of analyzing SSDs with penalized regression methods like the LASSO and Dantzig selector estimators. There exists much theoretical work for these methods that establish connections between their variable selection performance and properties of a fixed design matrix. Surprisingly, there has been little research on design criteria motivated by these connections and insights. In this talk, we discuss new approaches to both the design and analysis of SSDs that incorporates prior knowledge about the effect signs (positive/negative coefficients). Examples are given to show how these new designs compare to those found under established SSD criteria. A new Bayesian analysis is discussed that incorporates sign information and a simulation study is performed to show its ability to improve power over current methods.
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