Sensitivity measures, anova-like techniques and the use of bootstrap

Journal of Statistical Computation and Simulation

Volumn 58, Issue 2, 1997, Pages 99-120

  Archer, G E B ^a   Saltelli, A ^a   Sobol, I M ^b  

^a JOINT RESEARCH CENTRE   (Italy)

^b RUSSIAN ACADEMY OF SCIENCES   (Russian Federation)

Author keywords

Analysis of variance decomposition; Bootstrap; Sensitivity indices

Indexed keywords

EID: 0040052402     PISSN: 00949655     EISSN: None     Source Type: Journal    
DOI: 10.1080/00949659708811825     Document Type: Article

References (31)

1. Bratley, P. and Fox, B. L. (1988). Algorithm 659. Implementing Sobol's quaisrandom sequence generator. ACM Transactions on Mathematical Software, 14, 88-100.
2. Cotter, S. C. (1979). A screening design for factorial experiments with interactions. Biometrika, 66, 317-320.
3. Cox, D. C. (1982). An analytical method for uncertainty analysis of nonlinear output functions, with applications to Fault-tree analysis. IEEE Transactions on Reliability, R-31, 465-468.
4. Cukier, R. I., Fortuiri, C. M., Schuler, K. E., Petschek, A. G. and Schaibly, J. K. (1973). Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients. I Theory. J. Chem. Phys., 59, 3873-3878.
5. Davis, P. J. and Rabinowitz, P. (1984). Methods of numerical integration (2nd edition), Academic Press, New York.
6. Efron, B. (1992). Jackknife-after-bootstrap standard errors and influence functions (with discussion). Journal of the Royal Statistical Society, series B, 54, 83-127.
7. Efron, B. and Stein. C. (1981). The Jackknife estimate of variance, Annals of Statistics, 9, 586-596.
8. Efron and Tibshirani (1993). An Introduction to the Bootstrap. Chapman and Hall, New York.
9. Fisher, R. A. (1958). Statistical Methods for Research Workers (13th edition), Oliver and Boyd, Edinburgh.
10. Hall, P. (1986). On the number of bootstrap simulations required to construct a confidence interval. Annals of Statistics, 14, 1453-1462.
11. Hoefding, W. F. (1948). A class of statistics with asymptotically normal distributions. Annals of Mathematical Statistics, 19, 293-325.
12. Iman, R. L. and Conover, W. J. (1979). The use of rank trasform in regression. Technometrics, 21, 499-509.
13. Iman, R. L. and Hora, S. C. (1990). A robust measure of uncertainty importance for use in fault tree system analysis. Risk Analysis, 10, 401-406.
14. Krzykacz, B. (1990). SAMOS: A computer program for the derivation of empirical sensitivity measures of results from large computer models. Technical Report GRS-A-1700, Gesellschaft fuer Reaktor Sicherheit (GRS), MbH, Garching, Germany.
15. Liepman, D. and Stephanopoulos, G. (1985). Development and global sensitivity analysis of a closed ecosystem model. Ecological Modelling, 30, 13-47.
16. McKay, M. D. (1995). Evaluating Prediction Uncertainty. Los Alamos National Laborator Technical Report NUREG/GE-6311.
17. Sacks, J., Welch, S. J., Mitchell, T. J. and Wynn, H. P. (1989). Design and analysis of computer experiments. Statistical Science, 4, 409-435.
18. Saltelli, A., Andres, T. H. and Homma, T. (1993). Sensitivity Analysis of model output: an investigation of new techniques. Computational Statistics and Data Analysis, 15, 211-238.
19. Saltelli, A. and Bolado, R. (1996). Is there another way to compute Fourier Amplitude Sensitivity Test (FAST)? Submitted to Computational Statistics and Data Analysis.
20. Saltelli, A. and Hjorth, J. (1995). Uncertainty and sensitivity analyses of OH-initiated dimethylsulphide (DMS) oxidation and kinetics. J. Atmospheric Chemistry, 21, 187-221.
21. Saltelli, A. and Homma, T. (1992). Sensitivity analysis for model output. Performance of balckbox techniques on three international benchmark exercises. Computational Statistics and Data Analysis, 13.
22. Saltelli, A. and Marivoet, J. (1990) Nonparametric statistics in sensitivity analysis for model output; A comparison of selected techniques. Rel. Eng. and System Safety, 28, 229-253.
23. Saltelli, A. and Sobol', I. M. (1995a). Sensitivity analysis for nonlinear mathematical models: numerical experience. Matematicheskoye Modelirovaniye, 7, 16-29. (In Russian).
24. Saltelli, A. and Sobol', I. M. (1995b). About the use of rank transformation in sensitivity analysis of model output. Reliability Engineering and Systems Safety, 50, 225-239.
25. SAMO (1996). Proceedings of the Symposium on Theory and Applications of Sensitivity Analysis of Model Output in Computer Simulation (SAMO), Belgirate, Italy, September 1995. EUR Report 16331, ISBN 92-827-5530-4. Editors: A. Saltelli and H. Von Maravic', Luxembourg 1996.
26. Sobol', I. M. (1969). Multidimensional quadrature formulas and Haar functions, Nauka, Moscow. (In Russian).
27. Sobol', I. M. (1990a). Sensitivity estimates for nonlinear mathematical models, Matematicheskoe Modelirovanie, 2, 112-118 (in Russian), translated in Mathematical Modelling and Computational Experiments, 1, 407-414 (1993).
28. Sobol', I. M. (1990a). Sensitivity estimates for nonlinear mathematical models, Matematicheskoe Modelirovanie, 2, 112-118 (in Russian), translated in Mathematical Modelling and Computational Experiments, 1, 407-414 (1993).
29. Sobol', I. M. (1990b). Quasi-Monte Carlo methods. Progress in Nuclear Energy, 24 55-61.
30. Sobol', I. M. (1994). A Primer for the Monte Carlo Method. CRC Press, Boca Raton.
31. Sobol', I. M. and Shukhman, B. V. (1995). Integration with quasirandom sequences: numerical experiments. J. of Modern Phys. C., 263-275.