Global Sensitivity Analysis for Mixture Experiments

REFERENCES

• Claringbold , P. J. 1955 . “Use of the Simplex Design in the Study of Joint Action of Related Hormones,” . Biometrics , 11 : 174 – 185 .
   Web of Science ®Google Scholar
• Cornell , J. 2002 . Experiments with Mixtures. Designs, Models and the Analysis of Mixture Data , New York : Wiley .
   Google Scholar
• Coxeter , H. S. M. 1973 . Regular Polytopes , New York : Dover .
   Google Scholar
• Currin , C. , Mitchell , T. , Morris , M. and Ylvisaker , D. 1991 . “Bayesian Prediction of Deterministic Functions, With Applications to the Design and Analysis of Computer Experiments,” . Journal of the American Statistical Association , 86 : 953 – 963 .
   Web of Science ®Google Scholar
• Draguljić , D. , Dean , A. M. and Santner , T. J. 2012 . “Noncollapsing Space-Filling Designs for Bounded Nonrectangular Regions,” . Technometrics , 54 : 169 – 178 .
   Web of Science ®Google Scholar
• Gramacy , R. B. and Lee , H. K. H. 2012 . “Cases for the Nugget in Modeling Computer Experiments,” . Statistics and Computing , 22 : 713 – 722 .
   Web of Science ®Google Scholar
• Grundmann , A. and Moeller , M. 1978 . “Invariant Integration Formulas for the N-Simplex by Combinatorial Methods,” . SIAM Journal on Numerical Analysis , 15 : 282 – 290 .
   Web of Science ®Google Scholar
• Handcock , M. S. and Stein , M. L. 1993 . “A Bayesian Analysis of Kriging,” . Technometrics , 35 : 403 – 410 .
   Web of Science ®Google Scholar
• Higdon , D. , Gattiker , J. , Williams , B. and Rightley , M. 2008 . “Computer Model Calibration Using High-dimensional Output,” . Journal of the American Statistical Association , 103 : 570 – 583 .
   Web of Science ®Google Scholar
• Higdon , D. , Kennedy , M. , Cavendish , J. C. , Cafeo , J. A. and Ryne , R. D. 2004 . “Combining Field Data and Computer Simulation for Calibration and Prediction,” . SIAM Journal on Scientific Computing , 26 : 448 – 466 .
   Web of Science ®Google Scholar
• Kotz , S. , Johnson , N. L. and Balakrishnan , N. 2000 . Continuous Multivariate Distributions: Models and Applications , New York : Wiley .
   Google Scholar
• Linkletter , C. , Bingham , D. , Hengartner , N. , Higdon , D. and Ye , K. Q. 2006 . “Variable Selection for Gaussian Process Models in Computer Experiments,” . Technometrics , 48 : 478 – 490 .
   Web of Science ®Google Scholar
• Loeppky , J. L. , Sacks , J. and Welch , W. J. 2009 . “Choosing the Sample Size of a Computer Experiment: A Practical Guide,” . Technometrics , 51 : 366 – 376 .
   Web of Science ®Google Scholar
• Oakley , J. E. and O’Hagan , A. 2004 . “Probabilistic Sensitivity Analysis of Complex Models: A Bayesian Approach,” . Journal of the Royal Statistical Society, Series B , 66 : 751 – 769 .
   Web of Science ®Google Scholar
• O’Hagan , A. 1994 . Kendall’s Advanced Theory of Statistics: Volume 2B, Bayesian Analysis , London : Edward Arnold .
   Google Scholar
• Piepel , G. F. , Hicks , R. D. , Szychowski , J. M. and Loeppky , J. L. 2002 . “Methods for Assessing Curvature and Interaction in Mixture Experiments,” . Technometrics , 44 : 161 – 172 .
   Web of Science ®Google Scholar
• Pope , G. A. , Sepehrnoori , K. , Sharma , M. M. , McKinney , D. C. , Gerald , E. , Speitel , J. and Jackson , R. E. 1999 . “Three-Dimensional NAPL Fate Transport Model,” . Technical Report, United States Environmental Protection Agency, Ada, Oklahoma, US
   Google Scholar
• Pratola , M. 2006 . “Design on Non-Convex Regions: Optimal Experiments for Spatial Process Prediction,” . unpublished Master’s thesis, Department of Statistics and Actuarial Science, Simon Fraser University, Burnaby, British Columbia
   Google Scholar
• Prescott , P. 2008 . “Nearly Uniform Designs for Mixture Experiments,” . Communications in Statistics, Theory and Methods , 37 : 2095 – 2115 .
   Web of Science ®Google Scholar
• Sacks , J. , Welch , W. J. , Mitchell , T. J. and Wynn , H. P. 1989 . “Designs and Analysis of Computer Experiments” (with discussion), . Statistical Science , 4 : 409 – 435 .
   Google Scholar
• Saltelli , A. , Chan , K. and Scott , E. 2000 . Sensitivity Analysis , Chichester : Wiley .
   Google Scholar
• Santner , T. J. , Williams , B. J. and Notz , W. I. 2003 . The Design and Analysis of Computer Experiments , New York : Springer .
   Google Scholar
• Scheffé , H. 1958 . “Experiments with Mixtures,” . Journal of the Royal Statistical Society, Series B , 20 : 344 – 360 .
   Google Scholar
• Schonlau , M. and Welch , W. J. 2006 . “Screening the Input Variables to a Computer Model Via Analysis of Variance and Visualization,” . In Screening Methods for Experimentation in Industry, Drug Discovery and Genetics , Edited by: Dean , A. M. and Lewis , S. 308 – 327 . New York : Springer .
   Google Scholar
• Sobol’ , I. M. 1993 . “Sensitivity Analysis for Non-Linear Mathematical Models,” . Mathematical Modeling and Computational Experiment , 1 : 407 – 414 .
   Google Scholar