Target and Conditional Sensitivity Analysis with Emphasis on Dependence Measures
Whenever the functional relationship between a phenomenon and its determining factors is too complicated to be studied analytically, sensitivity analysis aims at determining with statistical tools which factors are the most important, and which are noninfluential.
During my post-doctoral mission at the French Commission for Atomic Energy, I have been brought to the idea of target and conditional sensitivity analysis, where one restricts the analysis to a specific domain of interest of the phenomenon. Although this has connection with studies of reliability, in which case the critical domain is usually a “failure domain”, this concept received so far surprisingly little attention in the literature.
In the classical probabilistic setting, uncertainties are taken into account by modeling the determining factors as random variables. In that context, sensitivity is related to statistical dependence, and measures of dependence seem the most versatile, powerful and promising tools. Such measures can take many forms and have been studied at diverse occasions, but they deserve more systematic study for the purpose of sensitivity analysis.
For these reasons, I had the opportunity to
- establish a review of methods akin to target and conditional sensitivity analysis;
- propose a simple, systematic framework for adapting existing tools;
- establish a review of classical dependence measures;
- establish a review of their use for sensitivity analysis;
- improve on some dependence measures, notably for sensitivity analysis;
- implement some of these tools in R; and
- illustrate numerically some of their properties.
Everything is detailed in my preprint (reference as BibTeX format).
This work was supervised by Amandine Marrel.
Moreover, I implemented every tools in R, interfaced with C++ for some routines, parallelized with OpenMP. The source code is available at the dedicated GitLab repository. Some of my former collaborators intend to wrap the code into the R package Sensitivity.