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Transformations and invariance in the sensitivity analysis of computer experiments
Author(s) -
Borgonovo E.,
Tarantola S.,
Plischke E.,
Morris M. D.
Publication year - 2014
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/rssb.12052
Subject(s) - monotonic function , estimator , invariant (physics) , transformation (genetics) , statistic , mathematics , test statistic , convergence (economics) , sensitivity (control systems) , computer science , statistical hypothesis testing , algorithm , statistics , mathematical analysis , biochemistry , chemistry , economics , mathematical physics , gene , economic growth , electronic engineering , engineering
Summary Monotonic transformations are widely employed in statistics and data analysis. In computer experiments they are often used to gain accuracy in the estimation of global sensitivity statistics. However, one faces the question of interpreting results that are obtained on the transformed data back on the original data. The situation is even more complex in computer experiments, because transformations alter the model input–output mapping and distort the estimators. This work demonstrates that the problem can be solved by utilizing statistics which are monotonic transformation invariant. To do so, we offer an investigation into the families of metrics either based on densities or on cumulative distribution functions that are monotonic transformation invariant and we introduce a new generalized family of metrics. Numerical experiments show that transformations allow numerical convergence in the estimates of global sensitivity statistics, both invariant and not, in cases in which it would otherwise be impossible to obtain convergence. However, one fully exploits the increased numerical accuracy if the global sensitivity statistic is monotonic transformation invariant. Conversely, estimators of measures that do not have this invariance property might lead to misleading deductions.