Related papers: Uncertainty Propagation and Bayesian Fusion on Uni…

Deep Learning (DL) methods have been transforming computer vision with innovative adaptations to other domains including climate change. For DL to pervade Science and Engineering (S&E) applications where risk management is a core component,…

Automatic prostate MRI segmentation faces persistent challenges due to inter-patient anatomical variability, blurred tissue boundaries, and distribution shifts arising from diverse imaging protocols. To address these issues, we propose…

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…

Quantification of uncertainty in production/injection forecasting is an important aspect of reservoir simulation studies. Conventional approaches include intrusive Galerkin-based methods (e.g., generalized polynomial chaos (gPC) and…

One of the big challenges in astrophysics is the comparison of complex simulations to observations. As many codes do not directly generate observables (e.g. hydrodynamic simulations), the last step in the modelling process is often a…

We study the fractal uncertainty principle in the joint time-frequency representation, and we prove a version for the Short-Time Fourier transform with Gaussian window on the modulation spaces. This can equivalently be formulated in terms…

For objects in the low Earth orbit region, uncertainty in atmospheric density estimation is an important source of orbit prediction error, which is critical for space situational awareness activities such as the satellite conjunction…

Uncertainty in large language model (LLM)-based systems is often studied at the level of a single model output, yet deployed LLM applications are compound systems in which uncertainty is transformed and reused across model internals,…

Ensemble disagreement is widely used as a proxy for epistemic uncertainty in medical image segmentation. In practice, many studies form ensembles via K-fold cross-validation (CV), yet refer to them as ``deep ensembles'' (DE). Because CV…

Majority of the text modelling techniques yield only point-estimates of document embeddings and lack in capturing the uncertainty of the estimates. These uncertainties give a notion of how well the embeddings represent a document. We…

In this paper, we prove the propagation of uniform upper bounds for the spatially homogeneous relativistic Boltzmann equation. These $L^\infty$ bounds have been known to be a challenging open problem in relativistic kinetic theory. To…

We apply a generic formalism of light propagation to linearly perturbed spherically symmetric dust models including a cosmological constant. For a comoving observer on the central worldline, we derive the equation of geodesic deviation and…

Many naturally-occuring models in the sciences are well-approximated by simplified models, using multiscale techniques. In such settings it is natural to ask about the relationship between inverse problems defined by the original problem…

The ensemble Kalman filter (EnKF) is a Monte Carlo approximation of the Kalman filter for high dimensional linear Gaussian state space models. EnKF methods have also been developed for parameter inference of static Bayesian models with a…

The transition density of a stochastic, logistic population growth model with multiplicative intrinsic noise is analytically intractable. Inferring model parameter values by fitting such stochastic differential equation (SDE) models to data…

We focus on the problem of uncertainty informed allocation of medical resources (vaccines) to heterogeneous populations for managing epidemic spread. We tackle two related questions: (1) For a compartmental ordinary differential equation…

Solving inverse problems without the use of derivatives or adjoints of the forward model is highly desirable in many applications arising in science and engineering. In this paper, we propose a new version of such a methodology, a framework…

In linear regression models, fusion of coefficients is used to identify predictors having similar relationships with a response. This is called variable fusion. This paper presents a novel variable fusion method in terms of Bayesian linear…

In this paper we review recently developed methods for nonparametric Bayesian inference for one-dimensional diffusion models. We discuss different possible prior distributions, computational issues, and asymptotic results.

Diffusion (score-based) generative models have been widely used for modeling various types of complex data, including images, audios, and point clouds. Recently, the deep connection between forward-backward stochastic differential equations…