Two-Stage Sensitivity-Based Group Screening in Computer Experiments

Sophisticated computer codes that implement mathematical models of physical processes can involve large numbers of inputs, and screening to determine the most active inputs is critical for understanding the input-output relationship. This article presents a new two-stage group screening methodology for identifying active inputs. In Stage 1, groups of inputs showing low activity are screened out; in Stage 2, individual inputs from the active groups are identified. Inputs are evaluated through their estimated total (effect) sensitivity indices (TSIs), which are compared with a benchmark null TSI distribution created from added low noise inputs. Examples show that, compared with other procedures, the proposed method provides more consistent and accurate results for high-dimensional screening. Additional details and computer code are provided in supplementary materials available online.

[1]  D. Altman,et al.  Statistics Notes: Diagnostic tests 1: sensitivity and specificity , 1994, BMJ.

[2]  Richard J. Beckman,et al.  A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a Computer Code , 2000, Technometrics.

[3]  Henry P. Wynn,et al.  Screening, predicting, and computer experiments , 1992 .

[4]  Dave Higdon,et al.  Combining Field Data and Computer Simulations for Calibration and Prediction , 2005, SIAM J. Sci. Comput..

[5]  Hugh A. Chipman,et al.  Prior Distributions for Bayesian Analysis of Screening Experiments , 2006 .

[6]  S. Lewis,et al.  Detection of interactions in experiments on large numbers of factors , 2001 .

[7]  Thomas J. Santner,et al.  Design and analysis of computer experiments for screening input variables , 2010 .

[8]  L. Stefanski,et al.  Controlling Variable Selection by the Addition of Pseudovariables , 2007 .

[9]  T. J. Mitchell,et al.  Two-Level Multifactor Designs for Detecting the Presence of Interactions , 1983 .

[10]  W. Welch.  ACED: Algorithms for the Construction of Experimental Designs , 1985 .

[11]  Russian Federation,et al.  On the use of variance reducing multipliers in Monte Carlo computations of a global sensitivity index , 1999 .

[12]  B. A. Worley.  Deterministic uncertainty analysis , 1987 .

[13]  Sonja Kuhnt,et al.  Design and analysis of computer experiments , 2010 .

[14]  Max D. Morris,et al.  An Overview of Group Factor Screening , 2006 .

[15]  A. Sterrett.  On the Detection of Defective Members of Large Populations , 1957 .

[16]  A. O'Hagan,et al.  Probabilistic sensitivity analysis of complex models: a Bayesian approach , 2004 .

[17]  Aaron L. Fogelson,et al.  Computational Modeling of Blood Clotting: Coagulation and Three-dimensional Platelet Aggregation , 2003 .

[18]  Angela M. Dean,et al.  TWO-STAGE GROUP SCREENING IN THE PRESENCE OF NOISE FACTORS AND UNEQUAL PROBABILITIES OF ACTIVE EFFECTS , 2005 .

[19]  R. Dorfman.  The Detection of Defective Members of Large Populations , 1943 .

[20]  A. Saltelli,et al.  Importance measures in global sensitivity analysis of nonlinear models , 1996 .

[21]  Thomas J. Santner,et al.  Algorithms for Generating Maximin Latin Hypercube and Orthogonal Designs , 2011 .

[22]  M. E. Johnson,et al.  Minimax and maximin distance designs , 1990 .

[23]  Max D. Morris,et al.  Sampling plans based on balanced incomplete block designs for evaluating the importance of computer model inputs , 2006 .

[24]  Runze Li,et al.  Design and Modeling for Computer Experiments , 2005 .

[25]  Jerome Sacks,et al.  Choosing the Sample Size of a Computer Experiment: A Practical Guide , 2009, Technometrics.

[26]  R. Fisher.  014: On the "Probable Error" of a Coefficient of Correlation Deduced from a Small Sample. , 1921 .

[27]  W. J. Conover,et al.  Practical Nonparametric Statistics , 1972 .

[28]  David Brunson,et al.  A Critical Assessment of Two-Stage Group Screening Through Industrial Experimentation , 2008, Technometrics.

[29]  Choosing Sample Size , 2022 .

[30]  Y. Benjamini,et al.  Controlling the false discovery rate: a practical and powerful approach to multiple testing , 1995 .

[31]  Karl Pearson,et al.  On the Probable Error of a Coefficient of Correlation as found from a Fourfold Table , 1913 .

[32]  T. Santner,et al.  Acetabular cup geometry and bone-implant interference have more influence on initial periprosthetic joint space than joint loading and surgical cup insertion. , 2006, Journal of Biomechanical Engineering.

[33]  Kenny Q. Ye,et al.  Variable Selection for Gaussian Process Models in Computer Experiments , 2006, Technometrics.

[34]  William J. Welch,et al.  Screening the Input Variables to a Computer Model Via Analysis of Variance and Visualization , 2006 .

[35]  Max D. Morris,et al.  Using Orthogonal Arrays in the Sensitivity Analysis of Computer Models , 2008, Technometrics.

[36]  Agus Sudjianto,et al.  Blind Kriging: A New Method for Developing Metamodels , 2008 .

[37]  G. Watson.  A Study of the Group Screening Method , 1961 .

[38]  Jack P. C. Kleijnen,et al.  Review of random and group-screening designs , 1987 .

[39]  D. Higdon,et al.  Computer Model Calibration Using High-Dimensional Output , 2008 .

[40]  Thomas J. Santner,et al.  Robust design for acetabular cup stability accounting for patient and surgical variability. , 2008, Journal of biomechanical engineering.