
Current theory of global sensitivity analysis, based on a nonlinear functional ANOVA decomposition of the random output, is limited in scope-for instance, the analysis is limited to the output's variance and the inputs have to be mutually independent-and leads to sensitivity indices the interpretation of which is not fully clear, especially interaction effects. Alternatively, sensitivity indices built for arbitrary user-defined importance measures have been proposed but a theory to define interactions in a systematic fashion and/or establish a decomposition of the total importance measure is still missing. It is shown that these important problems are solved all at once by adopting a new paradigm. By partitioning the inputs into those causing the change in the output and those which do not, arbitrary user-defined variability measures are identified with the outcomes of a factorial experiment at two levels, leading to all factorial effects without assuming any functional decomposition. To link various well-known sensitivity indices of the literature (Sobol indices and Shapley effects), weighted factorial effects are studied and utilized.
FOS: Computer and information sciences, Computer Science - Machine Learning, 330, [SPI] Engineering Sciences [physics], Machine Learning (stat.ML), interactions, [STAT.OT]Statistics [stat]/Other Statistics [stat.ML], factorial experiment, Machine Learning (cs.LG), Methodology (stat.ME), Statistics - Machine Learning, global sensitivity analysis, [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST], main effects, Sobol indices, Statistics - Methodology
FOS: Computer and information sciences, Computer Science - Machine Learning, 330, [SPI] Engineering Sciences [physics], Machine Learning (stat.ML), interactions, [STAT.OT]Statistics [stat]/Other Statistics [stat.ML], factorial experiment, Machine Learning (cs.LG), Methodology (stat.ME), Statistics - Machine Learning, global sensitivity analysis, [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST], main effects, Sobol indices, Statistics - Methodology
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