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Sensitivity analysis is an important tool used in many domains of computational science to either gain insight into the mathematical model and interaction of its parameters or study the uncertainty propagation through the input-output…
The Trotter-Suzuki decomposition is one of the main approaches for realization of quantum simulations on digital quantum computers. Variance-based global sensitivity analysis (the Sobol method) is a wide used method which allows to…
In a model of the form $Y=h(X_1,\ldots,X_d)$ where the goal is to estimate a parameter of the probability distribution of $Y$, we define new sensitivity indices which quantify the importance of each variable $X_i$ with respect to this…
For models evaluated at a random set of independent variables, the variance-based Shapley effects range between Sobol' indices, and the corresponding total indices admit derivative-based upper-bounds. Such relationships fail when the inputs…
In the context of global sensitivity analysis, the Sobol' indices constitute a powerful tool for assessing the relative significance of the uncertain input parameters of a model. We herein introduce a novel approach for evaluating these…
This article explores the generalized analysis-of-variance or ANOVA dimensional decomposition (ADD) for multivariate functions of dependent random variables. Two notable properties, stemming from weakened annihilating conditions, reveal…
We consider situations where data have been collected such that the sampling depends on the outcome of interest and possibly further covariates, as for instance in case-control studies. Graphical models represent assumptions about the…
Complex computer codes are widely used in science to model physical systems. Sensitivity analysis aims to measure the contributions of the inputs on the code output variability. An efficient tool to perform such analysis are the…
A general class of models is proposed that is able to estimate the whole predictive distribution of a dependent variable $Y$ given a vector of explanatory variables $\xb$. The models exploit that the strength of explanatory variables to…
Biomechanical models often need to describe very complex systems, organs or diseases, and hence also include a large number of parameters. One of the attractive features of physics-based models is that in those models (most) parameters have…
Inspired by the well-established variance-based methods for global sensitivity analysis, we develop a local total sensitivity index that decomposes the global total sensitivity conditions by independent variables' values. We employ this…
Sobol' sensitivity indices allow to quantify the respective effects of random input variables and their combinations on the variance of mathematical model output. We focus on the problem of Sobol' indices estimation via a metamodeling…
We present an HSIC-based approach for global sensitivity analysis of broad classes of models with correlated and possibly function-valued inputs and outputs. To this end, we define the total HSIC sensitivity index: a bounded, interpretable,…
This chapter makes a review, in a complete methodological framework, of various global sensitivity analysis methods of model output. Numerous statistical and probabilistic tools (regression, smoothing, tests, statistical learning, Monte…
Given-data methods for variance-based sensitivity analysis have significantly advanced the feasibility of Sobol' index computation for computationally expensive models and models with many inputs. However, the limitations of existing…
Traditionally, the sensitivity analysis of a Bayesian network studies the impact of individually modifying the entries of its conditional probability tables in a one-at-a-time (OAT) fashion. However, this approach fails to give a…
This paper explores the application of active learning strategies to adaptively learn Sobol indices for global sensitivity analysis. We demonstrate that active learning for Sobol indices poses unique challenges due to the definition of the…
Many mathematical models involve input parameters, which are not precisely known. Global sensitivity analysis aims to identify the parameters whose uncertainty has the largest impact on the variability of a quantity of interest. One of the…
Global sensitivity analysis of complex numerical models can be performed by calculating variance-based importance measures of the input variables, such as the Sobol indices. However, these techniques, requiring a large number of model…
Sensitivity analysis plays an important role in the development of computer models/simulators through identifying the contribution of each (uncertain) input factor to the model output variability. This report investigates different aspects…