Related papers: A flexible error estimate for the application of c…
We propose an analysis for the stabilized finite element methods proposed in, E. Burman, Stabilized finite element methods for nonsymmetric, noncoercive, and ill-posed problems. Part I: Elliptic equations. SIAM J. Sci. Comput., 35(6) 2013,…
We derive the extended fluctuation theorems in presence of multiple measurements and feedback, when the system is governed by Hamiltonian dynamics. We use only the forward phase space trajectories in the derivation. However, to obtain an…
Approximate group analysis technique, that is, the technique combining the methodology of group analysis and theory of small perturbations, is applied to finite-difference equations approximating ordinary differential equations.…
Mathematical methods provide useful framework for the analysis and design of complex systems. In newer contexts such as biology, however, there is a need to both adapt existing methods as well as to develop new ones. Using a combination of…
We study asymptotic properties of $M$-estimates of regression parameters in linear models in which errors are dependent. Weak and strong Bahadur representations of the $M$-estimates are derived and a central limit theorem is established.…
We consider the scenario where the parameters of a probabilistic model are expected to vary over time. We construct a novel prior distribution that promotes sparsity and adapts the strength of correlation between parameters at successive…
This article provides a new theory for the analysis of forward and backward particle approximations of Feynman-Kac models. Such formulae are found in a wide variety of applications and their numerical (particle) approximation are required…
We consider a perturbed integrable system with one frequency, and the approximate dynamics for the actions given by averaging over the angle. The classical theory grants that, for a perturbation of order epsilon, the error of this…
We consider a control-constrained optimal control problem subject to time-harmonic Maxwell's equations; the control variable belongs to a finite-dimensional set and enters the state equation as a coefficient. We derive existence of optimal…
Computer experiments with quantitative and qualitative inputs are widely used to study many scientific and engineering processes. Much of the existing work has focused on design and modeling or process optimization for such experiments.…
The paper is concerned with the Barenblatt-Biott model in the theory of poroelasticity. We derive a guaranteed estimate of the difference between exact and approximate solutions expressed in a combined norm that encompasses errors for the…
Changepoint detection is commonly formulated by minimizing the sum of in-sample losses to quantify the model's overall fit. However, for flexible modeling procedures -- especially those involving high-dimensional parameter spaces or…
The focus of this work is a posteriori error estimation for stochastic Galerkin approximations of parameter-dependent linear elasticity equations. The starting point is a three-field PDE model in which the Young's modulus is an affine…
A different general philosophy, to be called Full Randomness (FR), for the analysis of random effects models is presented, involving a notion of reducing or preferably eliminating fixed effects, at least formally. For example, under FR…
Forward and inverse models are used throughout different engineering fields to predict and understand the behaviour of systems and to find parameters from a set of observations. These models use root-finding and minimisation techniques…
A simple procedure to estimate O(alpha_s^3) and O(alpha_s^4) corrections to mass-dependent observables is conjectured. The method is tested in a number of cases where the O(alpha_s^3) contribution is exactly known, and reasonable agreement…
Stochastic computational models in the form of pure jump processes occur frequently in the description of chemical reactive processes, of ion channel dynamics, and of the spread of infections in populations. For spatially extended models,…
We adapt Stein's method to obtain Berry--Esseen type error bounds in the multivariate central limit theorem for non-stationary processes generated by time-dependent compositions of uniformly expanding dynamical systems. In a particular case…
Three key properties that are desired of trustworthy machine learning models deployed in high-stakes environments are fairness, explainability, and an ability to account for various kinds of "drift". While drifts in model accuracy, for…
This guide offers suggestions/insights on uncertainty quantification of nuclear structure models. We discuss a simple approach to statistical error estimates, strategies to assess systematic errors, and show how to uncover…