Bayesian analysis of definitive screening designs when the response is nonnormal

Abstract

Definitive screening designs (DSDs) are a class of experimental designs that allow the estimation of linear, quadratic, and interaction effects with little experimental effort if there is effect sparsity. The number of experimental runs is twice the number of factors of interest plus one. Many industrial experiments involve nonnormal responses. Generalized linear models (GLMs) are a useful alternative for analyzing these kind of data. The analysis of GLMs is based on asymptotic theory, something very debatable, for example, in the case of the DSD with only 13 experimental runs. So far, analysis of DSDs considers a normal response. In this work, we show a five‐step strategy that makes use of tools coming from the Bayesian approach to analyze this kind of experiment when the response is nonnormal. We consider the case of binomial, gamma, and Poisson responses without having to resort to asymptotic approximations. We use posterior odds that effects are active and posterior probability intervals for the effects and use them to evaluate the significance of the effects. We also combine the results of the Bayesian procedure with the lasso estimation procedure to enhance the scope of the method. Copyright © 2016 John Wiley & Sons, Ltd.