Related papers: Prior-informed Uncertainty Modelling with Bayesian…
One of the open problems in the field of forward uncertainty quantification (UQ) is the ability to form accurate assessments of uncertainty having only incomplete information about the distribution of random inputs. Another challenge is to…
Deep neural networks have achieved impressive results on a wide variety of tasks. However, quantifying uncertainty in the network's output is a challenging task. Bayesian models offer a mathematical framework to reason about model…
Bayesian analyses require that all variable model parameters are given a prior probability distribution. This can pose a challenge for analyses where multiple experiments are combined if these experiments use different parametrisations for…
Prior-data fitted networks (PFNs) have emerged as promising foundation models for prediction from tabular datasets, achieving state-of-the-art performance on small to moderate data sizes without tuning. While PFNs are motivated by Bayesian…
Equivariant models leverage prior knowledge on symmetries to improve predictive performance, but misspecified architectural constraints can harm it instead. While work has explored learning or relaxing constraints, selecting among…
Solving Bayesian inverse problems typically involves deriving a posterior distribution using Bayes' rule, followed by sampling from this posterior for analysis. Sampling methods, such as general-purpose Markov chain Monte Carlo (MCMC), are…
In the application of Bayesian methods to metrology, pre-data probabilities play a critical role in the estimation of the model uncertainty. Following the observation that distributions form Riemann's manifolds, methods of differential…
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…
Specifying a Bayesian prior is notoriously difficult for complex models such as neural networks. Reasoning about parameters is made challenging by the high-dimensionality and over-parameterization of the space. Priors that seem benign and…
Counterfactual explanations utilize feature perturbations to analyze the outcome of an original decision and recommend an actionable recourse. We argue that it is beneficial to provide several alternative explanations rather than a single…
In many inverse problems such as 3D X-ray Computed Tomography (CT), the estimation of an unknown quantity, such as a volume or an image, can be greatly enhanced, compared to maximum-likelihood techniques, by incorporating a prior model on…
We classify two types of Hierarchical Bayesian Model found in the literature as Hierarchical Prior Model (HPM) and Hierarchical Stochastic Model (HSM). Then, we focus on studying the theoretical implications of the HSM. Using examples of…
Uncertainty quantification plays an important role in achieving trustworthy and reliable learning-based computational imaging. Recent advances in generative modeling and Bayesian neural networks have enabled the development of…
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…
Despite substantial improvement in the development of forecasting approaches, conditional and dynamic uncertainty estimates ought to be accommodated in decision-making in power system operation and market, in order to yield either…
We present an approach to the simulation of quantum systems driven by classical stochastic processes that is based on the polynomial chaos expansion, a well-known technique in the field of uncertainty quantification. The polynomial chaos…
In many inverse problems, the unknown is composed of multiple components with different regularities, for example, in imaging problems, where the unknown can have both rough and smooth features. We investigate linear Bayesian inverse…
We propose a novel approach for estimating conditional or parametric expectations in the setting where obtaining samples or evaluating integrands is costly. Through the framework of probabilistic numerical methods (such as Bayesian…
Because of the complexity of fluid flow solvers, non-intrusive uncertainty quantification techniques have been developed in aerodynamic simulations in order to compute the quantities of interest required in an optimization process, for…
Bayesian methods have been very successful in quantifying uncertainty in physics-based problems in parameter estimation and prediction. In these cases, physical measurements y are modeled as the best fit of a physics-based model…