Measuring Inputs-Outputs Association for Time-Dependent Hazard Models Under Safety Objectives Using Kernels

Abstract

A methodology for assessing the inputs-outputs association for time-dependent predictive models subjected to safety objectives is investigated. Firstly, new dependency models for sampling random values of uncertain inputs that comply with the safety objectives are provided by making use of the desirability measures. Secondly, combining predictive risk models with such dependency models leads to the development of new kernel-based statistical tests of independence between the (safe) dynamic outputs and inputs. The associated test statistics are then normalized so as to introduce the first-order and total sensitivity indices that account for the desirability measures. Such indices rely on time-dependent sensitivity functionals (SFs) and kernel methods, which allow for treating nonstationary SFs as well as SFs having skewed or heavy-tailed distributions. Our approach is also well-suited for dynamic hazard models with prescribed copulas of inputs.

Optimal and Efficient Approximations of Gradients of Functions with Nonindependent Variables

“…Using the fact that X ∼ F, with F(x) ̸ = ∏ d j=1 F j (x j ), we are able to model X as follows [8][9][10][11][12]14,43]:…”

“…Nonindependent variables arise when at least two variables do not vary independently, and such variables are often characterized by their covariance matrices, distribution functions, copulas, and weighted distributions (see, e.g., [1][2][3][4][5][6][7]). Recently, dependency models provide explicit functions that link these variables together by means of additional independent variables [8][9][10][11][12]. Models with nonindependent input variables, including functions subjected to constraints, are widely encountered in different scientific fields, such as data analysis, quantitative risk analysis, and uncertainty quantification (see, e.g., [13][14][15]).…”

Optimal and efficient approximations of gradients of functions with non-independent variables

“…Non-independent variables arise when at least two variables do not vary independently, and such variables are often characterized by their covariance matrices, distribution functions, copulas, weighted distributions (see e.g., [1][2][3][4][5][6][7]). Recently, dependency models provide explicit functions that link these variables together by means of additional independent variables ( [8][9][10][11][12]). Models with nonindependent input variables, including functions subjected to constraints, are widely encountered in different scientific fields, such as data analysis, quantitative risk analysis, and uncertainty quantification (see e.g., [13][14][15]).…”