Transformations and invariance in the sensitivity analysis of computer experiments

• 成果类型: Article
• 署名作者: Borgonovo, E.; Tarantola, S.; Plischke, E.; Morris, M. D.
• 署名单位: Bocconi University; European Commission Joint Research Centre; EC JRC ISPRA Site; TU Clausthal; Iowa State University
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12052
• 发表日期: 2014
• 页码: 925-947
• 关键词: uncertainty importance; mathematical-models; tests; statistics; reduction; estimator; indexes; moment

摘要

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.