Joint Research Conference

June 24-26, 2014

Sequential Bayesian Analysis of Definitive Screening Experiments

Abstract:

 Definitive Screening experiments, Jones and Nachtsheim (2011), are experimental plans with three levels that allow the estimation of main effects, two factor interactions, and quadratic effects. Main effects are completely independent of two factor interactions, two factor interactions are not completely confounded with other two factor interactions, and quadratic effects are estimable. The number of experimental runs is just twice plus one the number of factors of interest. In order to analyze the results, Jones and Nachtsheim (2011) performed a forward stepwise regression in JMP, following Hamada and Wu (1992); they also used Akaike’s information criterion, (Hurvich and Tsai, 1989). In this work we show the sequential use of tools coming from the Bayesian approach to analyze this kind of experiments, namely: posterior distribution of effects, posterior odds that effects are active, and posterior probability intervals of the effects. We show that by combining all three tools leads to an improved identification of active effects in the experiment.