A Simple Bayesian Modification of D-Optimal Designs to Reduce Dependence on an Assumed Model

REFERENCES

• BBN Software Products . 1992 . RSIDiscover Reference Manual Cambridge , MA : Bolt Beranek Newman. .
   Google Scholar
• Bickel , P. J. and Doksum , K. A. 1977 . Mathematical Statistics: Basic Ideas and Selected Topics San Francisco : Holden-Day. .
   Google Scholar
• Box , G. E. P. and Draper , N. R. 1959 . “A Basis for the Selection of a Response Surface Design,” . Journal of the American Statistical Association , 54 : 622 – 654 .
   Web of Science ®Google Scholar
• Box , G. E. P. and Draper , N. R. 1987 . Empirical Model-Building and Response Surfaces New York : John Wiley. .
   Google Scholar
• Box , G. E. P. , Hunter , W. G. and Hunter , J. S. 1978 . Statistics for Experimenters New York : John Wiley. .
   Google Scholar
• Box , G. E. P. and Tiao , G. C. 1973 . Bayesian Inference in Statistical Analysis Reading , MA : Addison-Wesley. .
   Google Scholar
• Chaloner , K. 1984 . “Optimal Bayesian Experimental Design for Linear Models,” . The Annals of Statistics , 12 : 283 – 300 . Corrigendum 1985, 13, 836
   Web of Science ®Google Scholar
• Cook , R. D. and Nachtsheim , C. J. 1980 . “Comparison of Algorithms for Constructing Exact D-Optimal Designs,” . Technometrics , 22 : 315 – 324 .
   Web of Science ®Google Scholar
• Cook , R. D. and Nachtsheim , C. J. 1982 . “Model Robust, Linear-Optimal Designs,” . Technometrics , 24 : 49 – 54 .
   Web of Science ®Google Scholar
• Cook , R. D. and Nachtsheim , C. J. 1989 . “Computer-Aided Blocking of Factorial and Response-Surface Designs,” . Technometrics , 31 : 339 – 346 .
   Web of Science ®Google Scholar
• Cornell , J. A. 1990 . Experiments With Mixtures–Designs, Models, and the Analysis of Mixture Data, , 2nd ed. New York : John Wiley. .
   Google Scholar
• Draper , N. R. and Guttman , I. 1992 . “Treating Bias as Variance for Experimental Design Purposes,” . Annals of Institute of Statistical Mathematics , 44 : 659 – 671 .
   Web of Science ®Google Scholar
• Efron , B. and Morris , C. 1973 . “Stein's Estimation Rule and its Competitors–an Empirical Bayes Approach,” . Journal of the American Statistical Association , 68 : 117 – 130 .
   Web of Science ®Google Scholar
• Galil , Z. and Kiefer , J. 1977 . “Comparison of Box–Draper and D-Optimum Designs for Experiments With Mixtures,” . Technometrics , 19 : 441 – 444 .
   Web of Science ®Google Scholar
• Galil , Z. and Kiefer , J. 1980 . “Time and Space-Saving Computer Methods, Related to Mitchell's DETMAX, for Finding D-Optimum Designs,” . Technometrics , 21 : 301 – 313 .
   Google Scholar
• Hahn , G. , Meeker , W. and Feder , P. 1976 . “The Evaluation and Comparison of Experimental Designs for Fitting Regression Relationships,” . Journal of Quality Technology , 8 : 140 – 157 .
   Google Scholar
• Johnson , M. E. and Nachtsheim , C. J. 1983 . “Some Guidelines for Constructing Exact D-Optimal Designs on Convex Design Spaces,” . Technometrics , 25 : 271 – 277 .
   Web of Science ®Google Scholar
• Koch , D. , Morris , W. T. , Nachtsheim , C. J. and Welch , W. J. 1993 . “Computer Software for Robust Product Design,” University of Minnesota, Dept, of Operations and Management Science. . Working Paper 93–11
   Google Scholar
• Lee , P. M. 1989 . Bayesian Statistics: An Introduction New York : Oxford University Press. .
   Google Scholar
• Lindley , D. V. 1956 . “On a Measure of the Information Provided by an Experiment,” . The Annals of Mathematical Statistics , 27 : 986 – 1005 .
   Google Scholar
• Meyer , R. and Nachtsheim , C. J. 1991 . “The Coordinate Exchange Algorithm for Constructing Exact Optimal Experimental Designs,” University of Minnesota, Dept, of Operations and Management Science. . Working Paper 91–18
   Google Scholar
• Mitchell , T. J. 1974 . “An Algorithm for the Construction of D-Optimal Experimental Designs,” . Technometrics , 16 : 203 – 211 .
   Web of Science ®Google Scholar
• Montgomery , D. 1991 . Design and Analysis of Experiments New York : John Wiley. .
   Google Scholar
• Nachtsheim , C. J. 1987 . “Tools for Computer-Aided Design of Experiments,” . Journal of Quality Technology , 19 : 132 – 160 .
   Web of Science ®Google Scholar
• O'Hagan , A. 1978 . “Curve Fitting and Optimal Design for Prediction” . Journal of the Royal Statistical Society , 40 : 1 – 41 . (with discussion), Ser. B
   Google Scholar
• Oman , S. D. 1984 . “A Different Empirical Bayes Interpretation of Ridge and Stein Estimators,” . Journal of the Royal Statistical Society , 46 : 544 – 557 . Ser. B
   Google Scholar
• Piepel , G. F. 1988 . “Programs for Generating Extreme Vertices and Centroids of Linearly Constrained Experimental Regions,” . Journal of Quality Technology , 20 : 125 – 139 .
   Web of Science ®Google Scholar
• Pilz , J. 1991 . Bayesian Estimation and Experimental Design in Linear Regression Models New York : John Wiley. .
   Google Scholar
• St. John , R. C. and Draper , N. R. 1975 . “D-Optimality for Regression Designs: A Review,” . Technometrics , 17 : 15 – 23 .
   Web of Science ®Google Scholar
• Silvey , S. D. 1980 . Optimal Design London and New York : Chapman and Hall. .
   Google Scholar
• Smith , A. F. M. and Verdinelli , I. 1980 . “A Note on Bayes Designs for Inference Using a Hierarchical Linear Model,” . Biometrika , 67 : 613 – 619 .
   Web of Science ®Google Scholar
• Smith , G. and Campbell , F. 1980 . “A Critique of Some Ridge Regression Methods” . Journal of the American Statistical Association , 75 : 74 – 103 . (with discussion)
   Web of Science ®Google Scholar
• Snee , R. D. 1981 . “Developing Blending Models for Gasoline and Other Mixtures,” . Technometrics , 23 : 119 – 130 .
   Web of Science ®Google Scholar
• Snee , R. D. 1985 . “Computer Aided Design of Experiments–Practical Experiences,” . Journal of Quality Technology , 17 : 222 – 236 .
   Web of Science ®Google Scholar
• Steinberg , D. 1985 . “Model Robust Response Surface Designs: Scaling Two-Level Factorials,” . Biometrika , 72 : 513 – 526 .
   Web of Science ®Google Scholar
• Steinberg , D. and Hunter , W. 1984 . “Experimental Design: Review and Comment,” . Technometrics , 26 : 71 – 130 .
   Web of Science ®Google Scholar
• Vuchkov , I. N. 1977 . “A Ridge-Type Procedure for Design of Experiments,” . Biometrika , 64 : 147 – 150 .
   Web of Science ®Google Scholar
• Welch , W. J. 1982 . “Branch-and-Bound Search for Experimental Designs Based on D-Optimality and Other Criteria,” . Technometrics , 24 : 41 – 48 .
   Web of Science ®Google Scholar
• Welch , W. J. 1983 . “A Mean Squared Error Criterion for the Design of Experiments,” . Biometrika , 70 : 205 – 213 .
   Web of Science ®Google Scholar
• Wu , C. F. and Wynn , H. P. 1978 . “The Convergence of General Step-length Algorithms for Regular Optimum Design Criteria,” . The Annals of Statistics , 6 : 1276 – 1285 .
   Web of Science ®Google Scholar