2015 QPRC

Bayesian Analysis of Definitive Screening Designs With Nonnormal Responses.

Víctor M. Aguirre
Statistics Department,
Instituto Tecnológico Autónomo de México (ITAM)
 Río Hondo #1
México, D.F. 01080
MEXICO

Abstract:
    Definitive Screening Designs (DSDs) are a class of experimental designs that estimate linear, quadratic and interaction effects with little experimental effort. The main effects are completely independent of two factor interactions and quadratic effects. These interactions are not completely confounded with other interactions, and quadratic effects are estimable. 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 dubious for the DSD that takes into account six factors and and has only thirteen experimental runs. So far analysis of DSDs consider 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 experiments when the response is nonnormal. We consider the case of binomial, gamma and Poisson responses without having to resort to asymptotic approximations. The strategy takes into account the posterior distribution of effects, posterior odds that effects are active, and posterior probability intervals for the effects to evaluate significance of the effects.