Related papers: Posterior contraction rates for non-parametric sta…

Parameter identification problems in partial differential equations (PDEs) consist in determining one or more functional coefficient in a PDE. In this article, the Bayesian nonparametric approach to such problems is considered. Focusing on…

A scheme is developed for estimating state-dependent drift and diffusion coefficients in a stochastic differential equation from time-series data. The scheme does not require to specify parametric forms for the drift and diffusion…

Dynamical system state estimation and parameter calibration problems are ubiquitous across science and engineering. Bayesian approaches to the problem are the gold standard as they allow for the quantification of uncertainties and enable…

In this paper, we propose a non-parametric method for state estimation of high-dimensional nonlinear stochastic dynamical systems, which evolve according to gradient flows with isotropic diffusion. We combine diffusion maps, a manifold…

Posterior contractions rates (PCRs) strengthen the notion of Bayesian consistency, quantifying the speed at which the posterior distribution concentrates on arbitrarily small neighborhoods of the true model, with probability tending to 1 or…

We study the problem of efficiently computing the derivative of the fixed-point of a parametric nondifferentiable contraction map. This problem has wide applications in machine learning, including hyperparameter optimization, meta-learning…

We present an extension of local sensitivity analysis, also referred to as the perturbation approach for uncertainty quantification, to Bayesian inverse problems. More precisely, we show how moments of random variables with respect to the…

In this paper, the problem of state estimation, in the context of both filtering and smoothing, for nonlinear state-space models is considered. Due to the nonlinear nature of the models, the state estimation problem is generally intractable…

We address the problem of estimating unknown model parameters and state variables in stochastic reaction processes when only sparse and noisy measurements are available. Using an asymptotic system size expansion for the backward equation we…

This article investigates stochastic epidemic models with partial information and addresses the estimation of current values of not directly observable states. The latter is also called nowcasting and related to the so-called "dark figure"…

We consider a non-parametric Bayesian model for conditional densities. The model is a finite mixture of normal distributions with covariate dependent multinomial logit mixing probabilities. A prior for the number of mixture components is…

The paper is devoted to three-parametric self-similar Gaussian Volterra processes that generalize fractional Brownian motion. We study the asymptotic growth of such processes and the properties of long- and short-range dependence. Then we…

In this paper, we present a theoretical and computational workflow for the non-parametric Bayesian inference of drift and diffusion functions of autonomous diffusion processes. We base the inference on the partial differential equations…

We address the problem of estimating the uncertainty in the solution of power grid inverse problems within the framework of Bayesian inference. We investigate two approaches, an adjoint-based method and a stochastic spectral method. These…

In this letter, a new filtering technique to solve a nonlinear state estimation problem has been developed. It is well known that for a nonlinear system, the prior and posterior probability density functions (pdf) are non-Gaussian in…

This study addresses the well-posedness of a hemivariational inequality derived from the convective Brinkman-Forchheimer extended Darcy (CBFeD) model in both two and three dimensions. The CBFeD model describes the behavior of incompressible…

This paper studies the learning of linear operators between infinite-dimensional Hilbert spaces. The training data comprises pairs of random input vectors in a Hilbert space and their noisy images under an unknown self-adjoint linear…

We obtain exact asymptotic results for the disorder averaged persistence of a Brownian particle moving in a biased Sinai landscape. We employ a new method that maps the problem of computing the persistence to the problem of finding the…

A novel approximate Bayesian filter based on backward stochastic differential equations is introduced. It uses a nonlinear Feynman--Kac representation of the filtering problem and the approximation of an unnormalized filtering density using…

In this work, we present methods for state estimation in continuous-discrete nonlinear systems involving stochastic differential equations. We present the extended Kalman filter, the unscented Kalman filter, the ensemble Kalman filter, and…