Related papers: Data-Driven Uncertainty Quantification and Propaga…

We examine the problem of making reconciled forecasts of large collections of related time series through a behavioural/Bayesian lens. Our approach explicitly acknowledges and exploits the 'connectedness' of the series in terms of…

Due to the growing adoption of deep neural networks in many fields of science and engineering, modeling and estimating their uncertainties has become of primary importance. Despite the growing literature about uncertainty quantification in…

When analyzing real-world data it is common to work with event ensembles, which comprise sets of observations that collectively constrain the parameters of an underlying model of interest. Such models often have a hierarchical structure,…

Reduced-rank regression recognises the possibility of a rank-deficient matrix of coefficients. We propose a novel Bayesian model for estimating the rank of the coefficient matrix, which obviates the need for post-processing steps and allows…

Accurate overland runoff and infiltration predictions are critical for effective water resources management, in particular for urban flood management. However, the inherent uncertainty in rainfall patterns, soil properties, and initial…

For a Bayesian, real-time forecasting with the posterior predictive distribution can be challenging for a variety of time series models. First, estimating the parameters of a time series model can be difficult with sample-based approaches…

Bayesian inference allows machine learning models to express uncertainty. Current machine learning models use only a single learnable parameter combination when making predictions, and as a result are highly overconfident when their…

Deep unrolling is an emerging deep learning-based image reconstruction methodology that bridges the gap between model-based and purely deep learning-based image reconstruction methods. Although deep unrolling methods achieve…

This paper analyzes hierarchical Bayesian inverse problems using techniques from high-dimensional statistics. Our analysis leverages a property of hierarchical Bayesian regularizers that we call approximate decomposability to obtain…

The present paper proposes a novel Bayesian, computational strategy in the context of model-based inverse problems in elastostatics. On one hand we attempt to provide probabilistic estimates of the material properties and their spatial…

Application for semantic segmentation models in areas such as autonomous vehicles and human computer interaction require real-time predictive capabilities. The challenges of addressing real-time application is amplified by the need to…

Inverse Uncertainty Quantification (IUQ) method has been widely used to quantify the uncertainty of Physical Model Parameters (PMPs) in nuclear Thermal Hydraulics (TH) systems. This paper introduces a novel hierarchical Bayesian model which…

In recent years, machine learning has witnessed extensive adoption across various sectors, yet its application in medical image-based disease detection and diagnosis remains challenging due to distribution shifts in real-world data. In…

We discuss a general Bayesian framework on modeling multidimensional function-valued processes by using a Gaussian process or a heavy-tailed process as a prior, enabling us to handle nonseparable and/or nonstationary covariance structure.…

Differential equations based on physical principals are used to represent complex dynamic systems in all fields of science and engineering. Through repeated use in both academics and industry, these equations have been shown to represent…

Bayesian inference can quantify uncertainty in the predictions of neural networks using posterior distributions for model parameters and network output. By looking at these posterior distributions, one can separate the origin of uncertainty…

Joint modeling of spatially-oriented dependent variables is commonplace in the environmental sciences, where scientists seek to estimate the relationships among a set of environmental outcomes accounting for dependence among these outcomes…

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…

The analysis of parametric and non-parametric uncertainties of very large dynamical systems requires the construction of a stochastic model of said system. Linear approaches relying on random matrix theory and principal componant analysis…

Distribution regression has recently attracted much interest as a generic solution to the problem of supervised learning where labels are available at the group level, rather than at the individual level. Current approaches, however, do not…