Related papers: Gradient-enhanced global sensitivity analysis with…
Recent theoretical work in causal inference has explored an important class of variables which, when conditioned on, may further amplify existing unmeasured confounding bias (bias amplification). Despite this theoretical work, existing…
Compressive sensing has become a powerful addition to uncertainty quantification when only limited data is available. In this paper we provide a general framework to enhance the sparsity of the representation of uncertainty in the form of…
In uncertainty quantification, a stochastic modelling is often applied, where parameters are substituted by random variables. We investigate linear dynamical systems of ordinary differential equations with a quantity of interest as output.…
We develop new flexible univariate models for light-tailed and heavy-tailed data, which extend a hierarchical representation of the generalized Pareto (GP) limit for threshold exceedances. These models can accommodate departure from…
High-fidelity simulations and physical experiments are essential for engineering analysis and design, yet their high cost often makes two critical tasks--global sensitivity analysis (GSA) and optimization--prohibitively expensive. This…
In the past decade, Sobol's variance decomposition have been used as a tool - among others - in risk management. We show some links between global sensitivity analysis and stochastic ordering theories. This gives an argument in favor of…
The $\delta N$ formalism provides a powerful non-perturbative framework for following the evolution of primordial curvature perturbations on super-horizon scales. However, its standard implementation relies on the separate universe…
In this paper we develop elements of the global calculus of Fourier integral operators in $R^n$ under minimal decay assumptions on phases and amplitudes. We also establish global weighted Sobolev $L^2$ estimates for a class of Fourier…
Systems of the type $$\begin{cases} u_t = \nabla \cdot (D_1(u) \nabla u - S_1(u) \nabla v) + f_1(u, v),\\ v_t = \nabla \cdot (D_2(v) \nabla v + S_2(v) \nabla u) + f_2(u, v) \end{cases} \qquad (\star)$$ can be used to model pursuit-evasion…
In the context of uncertainty quantification, computational models are required to be repeatedly evaluated. This task is intractable for costly numerical models. Such a problem turns out to be even more severe for stochastic simulators, the…
Synthetic aperture radar (SAR) is an efficient and widely used remote sensing tool. However, data extracted from SAR images are contaminated with speckle, which precludes the application of techniques based on the assumption of additive and…
Recent financial disasters have emphasised the need to accurately predict extreme financial losses and their consequences for the institutions belonging to a given financial market. The ability of econometric models to predict extreme…
The non-parametric estimation of covariance lies at the heart of functional data analysis, whether for curve or surface-valued data. The case of a two-dimensional domain poses both statistical and computational challenges, which are…
We propose and assess a new global (derivative-free) optimization algorithm, inspired by the LIPO algorithm, which uses variance-based sensitivity analysis (Sobol indices) to reduce the number of calls to the objective function. This method…
While stochastic variational inference is relatively well known for scaling inference in Bayesian probabilistic models, related methods also offer ways to circumnavigate the approximation of analytically intractable expectations. The key…
This paper introduces a novel family of generalized exponentiated gradient (EG) updates derived from an Alpha-Beta divergence regularization function. Collectively referred to as EGAB, the proposed updates belong to the category of…
We introduce a new global sensitivity measure, the global activity scores. The measure is based on finite differences of the underlying function, in contrast to several sensitivity measures in the literature that are based on derivatives of…
Performing (variance-based) global sensitivity analysis (GSA) with dependent inputs has recently benefited from cooperative game theory concepts.By using this theory, despite the potential correlation between the inputs, meaningful…
Given a bivariate random pair $(X,Y)$, a natural problem is to estimate, from a single sample $(X_i,Y_i)_{1\le i\le n}$, quantities such as $\mathbb{E}\left[ \mathbb{E}[ Y\mid X ]^2 \right]$. More broadly, sensitivity indices are designed…
We develop flexible methods of deriving variational inference for models with complex latent variable structure. By splitting the variables in these models into "global" parameters and "local" latent variables, we define a class of…