A Bayesian Approach to the Analysis of Industrial Experiments: An Illustration with Binomial Count Data

ABSTRACT

In recent years, Bayesian methods have become increasingly popular for solving industrial statistical problems. In this article, we illustrate the use of Bayesian methods to analyze binomial count data collected from a designed experiment. In addition to fitting an appropriate logistic regression model, we show how the Bayesian approach provides an integrated framework to address model goodness-of-fit, model selection, response surface estimation, optimization, and prediction.

KEYWORDS:

• Bayesian χ² goodness-of-fit test
• Bayesian information criterion
• contour plot
• experimental factor
• factorial design
• logistic regression
• Markov chain Monte Carlo
• optimal factor level
• prediction
• response surface

ACKNOWLEDGEMENTS

B. Weaver's work was partially funded by NSF grant DMS #0502347 EMSW21-RTG awarded to the Department of Statistics, Iowa State University. M. Hamada thanks C. C. Essix for her support and encouragement.

Additional information

Notes on contributors

Brian P. Weaver

B. P. Weaver is a graduate student and holds a B.S. in Mathematics from the University of New Mexico. His research interests include reliability and astrostatistics.

Michael S. Hamada

M. S. Hamada is a Technical Staff Member and holds a Ph.D. in Statistics from the University of Wisconsin-Madison. His research interests include design and analysis experiments, quality control, and reliability.