相关论文: Continuity of the Solution of a Non-Parametric Bay…

In the present paper we consider the varying coefficient model which represents a useful tool for exploring dynamic patterns in many applications. Existing methods typically provide asymptotic evaluation of precision of estimation…

In the present work, a rate-dependent cohesive zone model for the fracture of polymeric interfaces is presented. Inverse calibration of parameters for such complex models through trial and error is computationally tedious due to the large…

Current methods for regularization in machine learning require quite specific model assumptions (e.g. a kernel shape) that are not derived from prior knowledge about the application, but must be imposed merely to make the method work. We…

This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems by framing the problem in a stochastic optimization setting. By doing so, we show that many randomized methods are variants of a…

When a mathematical or computational model is used to analyse some system, it is usual that some parameters resp.\ functions or fields in the model are not known, and hence uncertain. These parametric quantities are then identified by…

In this work, we develop a Bayesian framework for solving inverse problems in which the unknown parameter belongs to a space of Radon measures taking values in a separable Hilbert space. The inherent ill-posedness of such problems is…

Our understanding of physical systems generally depends on our ability to match complex computational modelling with measured experimental outcomes. However, simulations with large parameter spaces suffer from inverse problem instabilities,…

Univariate or multivariate ordinal responses are often assumed to arise from a latent continuous parametric distribution, with covariate effects which enter linearly. We introduce a Bayesian nonparametric modeling approach for univariate…

We discuss a recently developed formalism which describes the quantum evolution of a solid-state qubit due to its continuous measurement. In contrast to the conventional ensemble-averaged formalism, it takes into account the measurement…

We analyze the Ensemble and Polynomial Chaos Kalman filters applied to nonlinear stationary Bayesian inverse problems. In a sequential data assimilation setting such stationary problems arise in each step of either filter. We give a new…

Multi-class classification methods that produce sets of probabilistic classifiers, such as ensemble learning methods, are able to model aleatoric and epistemic uncertainty. Aleatoric uncertainty is then typically quantified via the Bayes…

Sensors in high-precision mechatronic systems require accurate calibration, which is achieved using test beds that, in turn, require even more accurate calibration. The aim of this paper is to develop a cascaded calibration method for…

Assimilation of continuously streamed monitored data is an essential component of a digital twin; the assimilated data are used to ensure the digital twin is a true representation of the monitored system. One way this is achieved is by…

Variational Bayes (VB) has been used to facilitate the calculation of the posterior distribution in the context of Bayesian inference of the parameters of nonlinear models from data. Previously an analytical formulation of VB has been…

Bayesian methods are a popular choice for statistical inference in small-data regimes due to the regularization effect induced by the prior. In the context of density estimation, the standard nonparametric Bayesian approach is to target the…

A density estimation method in a Bayesian nonparametric framework is presented when recorded data are not coming directly from the distribution of interest, but from a length biased version. From a Bayesian perspective, efforts to…

A mathematical model is a function taking certain arguments and returning a theoretical prediction of a feature of a physical system. The arguments to the mathematical model can be split into two groups; (a) controllable variables of the…

When dealing with Bayesian inference the choice of the prior often remains a debatable question. Empirical Bayes methods offer a data-driven solution to this problem by estimating the prior itself from an ensemble of data. In the…

The simulation of physical phenomena with computer models relies on the estimation of physical and/or numerical parameters calibrated to fit experimental data. The approximations within the computer model and the errors in the measurements…

This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…