Bayesian Variable Selection for Fractional Factorial Experiments with Multilevel Categorical Factors

References

• Box, G. and Meyer, R. D. (1986). “An Analysis for Unreplicated Fractional Factorials”. Technometrics 28, pp. 11–18.
   Web of Science ®Google Scholar
• Box, G. and Meyer, R. D. (1993). “Finding the Active Factors in Fractioned Screening Experiments”. Journal of Quality Technology 25, pp. 94–105.
   Web of Science ®Google Scholar
• Chipman, H. (1996). “Bayesian Variable Selection with Related Predictors”. The Canadian Journal of Statistics 24 (1), pp. 17–36.
   Web of Science ®Google Scholar
• Chipman, H.; Hamada, M.; and Wu, C. F. J. (1997). “A Bayesian Variable-Selection Approach for Analyzing Designed Experiments with Complex Aliasing”. Technometrics 39 (4), pp. 372–381.
   Web of Science ®Google Scholar
• Daniel, C. (1959). “Use of Half-Normal Plots in Interpreting Factorial Two Level Experiments”. Technometrics 1, pp. 311–341.
   Google Scholar
• Davis, T. P. (1995). “Analysis of an Experiment Aimed at Improving the Reliability of Transmission Centre Shafts”. Lifetime Data Analysis 1, pp. 275–306.
   Google Scholar
• Dobson, A. J. (1988). An Introduction to Statistical Modelling. New York, NY: Chapman and Hall.
   Google Scholar
• Draper, D. (1995). “Assessment and Propagation of Model Uncertainty”. Journal of the Royal Statistical Society, Series B 57 (1), pp. 45–97.
   Google Scholar
• Draper, N. R. and Smith, H. (1981). Applied Regression Analysis, 2nd edition. New York, NY: John Wiley # Sons Inc.
   Google Scholar
• Fernandez, C.; Ley, E.; and Steel, M. F. J. (2001). “Benchmark Priors for Bayesian Model Averaging”. Journal of Econometrics 100 (2), pp. 381–427.
   Web of Science ®Google Scholar
• Gelman, A.; Carlin, J.; Stern, H.; and Rubin, D. (2004). Bayesian Data Analysis, 2nd edition. Boca Raton, FL: CRC Press/Chapman and Hall.
   Google Scholar
• George, E. I. and McCulloch, R. E. (1993). “Variable Selection via Gibbs Sampling”. Journal of the American Statistical Association 88, pp. 881–889
   Web of Science ®Google Scholar
• Gilks, W. R.; Richardson, S.; and Spiegelhalter, D. J., (eds.) (1996). Markov Chain Monte Carlo in Practice. London, UK: Chapman and Hall.
   Google Scholar
• Green, P. J. (1995). “Reversible Jump Markov Chain Monte Carlo Computations and Bayesian Model Determination”. Biometrika 82, pp. 711–732.
   Web of Science ®Google Scholar
• Hamada, M. and Wu, C. F. J. (1992). “Analysis of Designed Experiments with Complex Aliasing”. Journal of Quality Technology 24, pp. 130–137.
   Web of Science ®Google Scholar
• Henkin, E. (1986). “The Reduction of Variability of Blood Glucose Levels”. In Fourth Supplier Symposium on Taguchi Methods, pp. 758–785. Dearborn, MI: American Supplier Institute.
   Google Scholar
• Joseph, V. R. and Delaney, J. D. (2007). “Functionally Induced Priors for the Analysis of Experiments”. Technometrics 49, pp. 1–11.
   Web of Science ®Google Scholar
• Lindley, D. V. and Smith, A. F. M. (1972). “Bayes Estimates for the Linear Model (with Discussion)”. Journal of the Royal Statistical Society, Series B 34, pp. 1–42.
   Google Scholar
• Lunn, D. J.; Thomas, A.; Best, N.; and Spiegelhalter, D. (2000) “WinBUGS–A Bayesian Modelling Framework: Concepts, Structure, and Extensibility”. Statistics and Computing 10, pp. 325–337.
   Web of Science ®Google Scholar
• Meyer, R. D. and Wilkinson, R. G. (1998). “Bayesian Variable Assessment”. Communications in Statistics–Theory and Methods 27 (11), pp. 2675–2705.
   Web of Science ®Google Scholar
• Nobile, A. and Green, P. J. (2000). “Bayesian Analysis of Factorial Experiments by Mixture Modelling”. Biometrika 87 (1), pp. 15–35.
   Google Scholar
• Raftery, A. E.; Madigan, D.; and Hoeting, J. A. (1997). “Bayesian Model Averaging for Linear Regression Models”. Journal of the American Statistical Association 92, pp. 179–191.
   Web of Science ®Google Scholar
• Smith, A. F. M. (1986). “Some Bayesian Thoughts on Modelling and Model Choice”. The Statistician 35, pp. 97–102.
   Google Scholar
• Spiegelhalter, D.; Abrams, K.; and Myles, J. (2004). Bayesian Approaches to Clinical Trials and Health-Care Evaluation. New York, NY: John Wiley # Sons.
   Google Scholar
• Spiegelhalter, D.; Thomas, A.; Best, N.; and Lunn, D. (2003). WinBUGS User Manual, Version 1.4. Cambridge, UK: MRC Biostatistcs Unit.
   Google Scholar
• Woodward, P. (2005). “BugsXLA. Bayes for the Common Man”. Journal of Statistical Software 14 (5). http://www.jstatsoft.org/
   Google Scholar
• Wu, C. F. J. and Hamada, M. (2000). Experiments. Planning, Analysis and Parameter Design Optimization. New York, NY: John Wiley # Sons.
   Google Scholar
• Zellner, A. (1986). “On Assessing Prior Distributions and Bayesian Regression Analysis with g-Prior Distributions”. In Bayesian Inference and Decision Techniques: Essays in Honour of Bruno de Finetti, P. K. Goel and A. Zellner, eds., pp. 233–243. Amsterdan: North-Holland.
   Google Scholar