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Theory and Methods

Bayes Optimal Designs for Two- and Three-Level Factorial Experiments

Pages 937-946 | Received 01 Oct 1991, Published online: 27 Feb 2012

References

  • Box , G. E. P. and Draper , N. R. 1987 . Empirical Model-Building and Response Surfaces , New York : John Wiley .
  • Chaloner , K. 1984 . “Optimal Bayesian Experimental Designs for Linear Models,” . The Annals of Mathematical Statistics , 12 : 283 – 300 .
  • Cochran , W. and Cox , G. 1950 . Experimental Designs , New York : John Wiley .
  • Gupta , A. Das and Studden , W. J. 1991 . “Robust Bayesian Experimental Designs in Normal Linear Models,” . The Annals of Statistics , 19 : 1244 – 1256 .
  • DuMouchel , W. H. 1988 . “A Bayesian Model and a Graphical Elicitation Procedure for Multiple Comparisons,” . Bayesian Statistics , 3 : 127 – 146 .
  • Duncan , G. and DeGroot , M. H. “A Mean Squared Error Approach to Optimal Design Theory,” . Proceedings of the 1976 Conference on Information: Sciences and Systems . pp. 217 – 221 . The Johns Hopkins University .
  • El-Kruntz , S. and Studden , W. J. 1991 . “Bayesian Optimal Designs for Linear Regression Models,” . The Annals of Statistics , 19 : 2183 – 2208 .
  • Garthwaite , P. H. and Dickey , J. M. 1988 . “Quantifying Expert Opinion in Linear Regression Problems,” . The Journal of the Royal Statistical Society , 50 : 462 – 474 . Ser. B
  • Giovagnoli , A. and Verdinelli , I. 1983 . “Bayes D-Optimal and E-Optimal Block Designs,” . Biometrika , 70 : 695 – 706 .
  • Giovagnoli , A. and Verdinelli , I. 1985 . “Optimal Block Designs Under a Hierarchical Linear Model,” . Bayesian Statistics , 2 : 655 – 662 .
  • Giovagnoli , A. and Wynn , H. P. 1985 . “G-Majorization with Applications to Matrix Orderings,” . Linear Algebra and Its Applications , 67 : 111 – 135 .
  • John , P. J. 1971 . Statistical Design and Analysis of Experiments , New York : Macmillan .
  • John , P. J. 1990 . Statistical Methods in Engineering and Quality Assurance , New York : John Wiley .
  • Kadane , J. B. , Dickey , J. M. , Winkler , R. L. , Smith , W. S. and Peters , S. C. 1980 . “Interactive Elicitation of Opinion for a Normal Linear Model,” . Journal of the American Statistical Association , 75 : 845 – 854 .
  • Kolyva-Machera , F. 1989 . “D-optimality in 3k Designs for N = 1 mod9 Observations,” . Journal of Statistical Planning and Inference , 22 : 95 – 103 .
  • Owen , R. J. 1970 . “The Optimum Design of a Two-Factor Experiment Using Prior Information,” . The Annals of Mathematical Statistics , 41 : 1917 – 1934 .
  • Pilz , J. 1983 . Bayesian Estimation and Experimental Design in Linear Regression , Teubner-Texte zur Mathematik , Leipzig : Teubner-Verlag .
  • Searle , S. R. 1971 . Linear Models , New York : John Wiley .
  • Smith , A. F. M. and Verdinelli , I. 1980 . “A Note on Bayes Designs for Inference Using a Hierarchical Linear Model,” . Biometrika , 67 : 613 – 619 .
  • Toman , B. and Notz , W. 1991 . “Bayesian Optimal Experimental Design for Treatment-Control Comparisons in the Presence of Two-Way Heterogeneity,” . Journal of Statistical Planning and Inference , 27 : 51 – 63 .
  • Tong , Y. L. 1990 . The Multivariate Normal Distribution , New York : Springer-Verlag .
  • Yates , F. 1937 . The Design and Analysis of Factorial Experiments , Hapenden , , UK : Imperial Bureau of Soil Science .

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