Related papers: A computational spectral approach to interest rate…
We introduce an R package for Bayesian modeling and uncertainty quantification for problems involving count ratios. The modeling relies on the assumption that the quantity of interest is the ratio of Poisson means rather than the ratio of…
An essential ingredient of a spectral method is the choice of suitable bases for test and trial spaces. On complex domains, these bases are harder to devise, necessitating the use of domain partitioning techniques such as the spectral…
Partial differential equations (PDEs) are fundamental across numerous scientific fields. As these problems scale to high dimensions, classical numerical schemes introduce severe computational bottlenecks, known as the curse of…
Inverse Uncertainty Quantification (IUQ) method has been widely used to quantify the uncertainty of Physical Model Parameters (PMPs) in nuclear Thermal Hydraulics (TH) systems. This paper introduces a novel hierarchical Bayesian model which…
Missing data is a common challenge in biomedical research. This fact, along with growing dataset volumes of the modern era, make the issue of computationally-efficient analysis with missing data of crucial practical importance. A general…
We propose a general framework for quantum error mitigation that combines and generalizes two techniques: probabilistic error cancellation (PEC) and zero-noise extrapolation (ZNE). Similarly to PEC, the proposed method represents ideal…
Physics-Informed Neural Networks (PINNs) have been widely used to obtain solutions to various physical phenomena modeled as Differential Equations. As PINNs are not naturally equipped with mechanisms for Uncertainty Quantification, some…
Ensembles of General Circulation Models (GCMs) are the primary tools for investigating climate sensitivity, projecting future climate states, and quantifying uncertainty. GCM ensembles are subject to substantial uncertainty due to model…
The requirement to generate robust robotic platforms is a critical enabling step to allow such platforms to permeate safety-critical applications (i.e., the localization of autonomous platforms in urban environments). One of the primary…
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…
Data-driven discovery of partial differential equations (PDEs) has emerged as a promising approach for deriving governing physics when domain knowledge about observed data is limited. Despite recent progress, the identification of governing…
In this work we introduce a manifold learning-based method for uncertainty quantification (UQ) in systems describing complex spatiotemporal processes. Our first objective is to identify the embedding of a set of high-dimensional data…
We consider a model selection estimator of the covariance of a random process. Using the Unbiased Risk Estimation (URE) method, we build an estimator of the risk which allows to select an estimator in a collection of model. Then, we present…
We prove convergence rates of linear sampling recovery of functions in abstract Bochner spaces satisfying weighted summability of their generalized polynomial chaos expansion coefficients. The underlying algorithm is a function-valued…
On a daily investment decision in a security market, the price earnings (PE) ratio is one of the most widely applied methods being used as a firm valuation tool by investment experts. Unfortunately, recent academic developments in financial…
This paper explores the versatility and depth of Bayesian modeling by presenting a comprehensive range of applications and methods, combining Markov chain Monte Carlo (MCMC) techniques and variational approximations. Covering topics such as…
We present a framework for constructing multivariate risk measures that is inspired from univariate Optimized Certainty Equivalent (OCE) risk measures. We show that this new class of risk measures verifies the desirable properties such as…
A widely used method to create a continuous representation of a discrete data-set is regression analysis. When the regression model is not based on a mathematical description of the physics underlying the data, heuristic techniques play a…
This work proposes a method for sparse polynomial chaos (PC) approximation of high-dimensional stochastic functions based on non-adapted random sampling. We modify the standard l1 -minimization algorithm, originally proposed in the context…
Polynomial chaos expansion is a popular way to develop surrogate models for stochastic systems with arbitrary random variables. Standard techniques such as Galerkin projection, stochastic collocation, and least squares approximation, are…