Bayesian Analysis of Two-Level Fractional Factorial Experiments with Non-Normal Responses

Abstract

An intractable issue on screening experiments is to identify significant effects and to select the best model when the number of factors is large, especially for fractional factorial experiments with non-normal responses. In such cases, a three-stage Bayesian approach based on generalized linear models (GLMs) is proposed to identify which effects should be included in the target model where the principles of effect sparsity, hierarchy, and heredity are successfully considered. Three simulation experiments with non-normal responses which follow Poisson, binomial, and gamma distributions are presented to illustrate the performance of the proposed approach.

Keywords:

• Bayesian analysis
• Fractional factorial experiment
• Generalized linear models
• Non-normal response

Mathematics Subject Classification:

• 62K15
• 62F15

Acknowledgments

The authors are grateful to the editors and the anonymous reviewers for their insightful comments on earlier versions that helped improve the article. The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China (NSFC) under grant 70931002.