Related papers: Inverse Problems in a Bayesian Setting

In a Bayesian setting, inverse problems and uncertainty quantification (UQ) - the propagation of uncertainty through a computational (forward) model - are strongly connected. In the form of conditional expectation the Bayesian update…

In nuclear reactor system design and safety analysis, the Best Estimate plus Uncertainty (BEPU) methodology requires that computer model output uncertainties must be quantified in order to prove that the investigated design stays within…

Inverse Uncertainty Quantification (UQ), or Bayesian calibration, is the process to quantify the uncertainties of random input parameters based on experimental data. The introduction of model discrepancy term is significant because…

Inverse problems defined naturally on the sphere are becoming increasingly of interest. In this article we provide a general framework for evaluation of inverse problems on the sphere, with a strong emphasis on flexibility and scalability.…

Uncertainty quantification (UQ) is the process of systematically determining and characterizing the degree of confidence in computational model predictions. In the context of systems biology, especially with dynamic models, UQ is crucial…

These lecture notes highlight the mathematical and computational structure relating to the formulation of, and development of algorithms for, the Bayesian approach to inverse problems in differential equations. This approach is fundamental…

The Best Estimate plus Uncertainty (BEPU) approach for nuclear systems modeling and simulation requires that the prediction uncertainty must be quantified in order to prove that the investigated design stays within acceptance criteria. A…

An evolutionary form of a generalized Bayesian update method, which is strictly derivative- free yet directed through an additive update term based purely on the statistical moments of the design variables, is proposed for nonlinear inverse…

This paper focuses on inverse problems to identify parameters by incorporating information from measurements. These generally ill-posed problems are formulated here in a probabilistic setting based on Bayes's theorem because it leads to a…

Inverse problems aim to determine model parameters of a mathematical problem from given observational data. Neural networks can provide an efficient tool to solve these problems. In the context of Bayesian inverse problems, Uncertainty…

We develop a generative model-based approach to Bayesian inverse problems, such as image reconstruction from noisy and incomplete images. Our framework addresses two common challenges of Bayesian reconstructions: 1) It makes use of complex,…

Due to their intuitive appeal, Bayesian methods of modeling and uncertainty quantification have become popular in modern machine and deep learning. When providing a prior distribution over the parameter space, it is straightforward to…

In inverse problems, uncertainty quantification (UQ) deals with a probabilistic description of the solution nonuniqueness and data noise sensitivity. Setting seismic imaging into a Bayesian framework allows for a principled way of studying…

The Bayesian approach to inverse problems provides a practical way to solve ill-posed problems by augmenting the observation model with prior information. Due to the measure-theoretic underpinnings, the approach has raised theoretical…

Bayesian optimization is a coherent, ubiquitous approach to decision-making under uncertainty, with applications including multi-arm bandits, active learning, and black-box optimization. Bayesian optimization selects decisions (i.e.…

In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…

Inverse problems play a key role in modern image/signal processing methods. However, since they are generally ill-conditioned or ill-posed due to lack of observations, their solutions may have significant intrinsic uncertainty. Analysing…

Machine learning methods for computational imaging require uncertainty estimation to be reliable in real settings. While Bayesian models offer a computationally tractable way of recovering uncertainty, they need large data volumes to be…

This paper proposes a novel uncertainty quantification framework for computationally demanding systems characterized by a large vector of non-Gaussian uncertainties. It combines state-of-the-art techniques in advanced Monte Carlo sampling…

This paper introduces CUQIpy, a versatile open-source Python package for computational uncertainty quantification (UQ) in inverse problems, presented as Part I of a two-part series. CUQIpy employs a Bayesian framework, integrating prior…