Related papers: Uncertainty Propagation and Bayesian Fusion on Uni…
This paper addresses uncertainty propagation on unimodular matrix Lie groups that have a surjective exponential map. We derive the exact formula for the propagation of mean and covariance in a continuous-time setting from the governing…
We address the problem of uncertainty propagation in the discrete Fourier transform by modeling the fast Fourier transform as a factor graph. Building on this representation, we propose an efficient framework for approximate Bayesian…
Coupled partial differential equation (PDE) systems, which often represent multi-physics models, are naturally suited for modular numerical solution methods. However, several challenges yet remain in extending the benefits of modularization…
This paper deals with uncertainty propagation of general stochastic hybrid systems (GSHS) where the continuous state space is a compact Lie group. A computational framework is proposed to solve the Fokker-Planck (FP) equation that describes…
Latent factor models are widely used to discover and adjust for hidden variation in modern applications. However, most methods do not fully account for uncertainty in the latent factors, which can lead to miscalibrated inferences such as…
The problem of filtering - propagation of states through stochastic differential equations (SDEs) and association of measurement data using Bayesian inference - in a state space which forms a Lie group is considered. Particular emphasis is…
This paper introduces a global uncertainty propagation scheme for rigid body dynamics, through a combination of numerical parametric uncertainty techniques, noncommutative harmonic analysis, and geometric numerical integration. This method…
This paper presents a novel mathematical framework for representing uncertainty in large deformation diffeomorphic image registration. The Bayesian posterior distribution over the deformations aligning a moving and a fixed image is…
Ensemble Kalman Inversion (EKI) has been a very popular algorithm used in Bayesian inverse problems. It samples particles from a prior distribution, and introduces a motion to move the particles around in pseudo-time. As the pseudo-time…
A multifidelity method for the nonlinear propagation of uncertainties in the presence of stochastic accelerations is presented. The proposed algorithm treats the uncertainty propagation (UP) problem by separating the propagation of the…
This paper addresses the Bayesian calibration of dynamic models with parametric and structural uncertainties, in particular where the uncertain parameters are unknown/poorly known spatio-temporally varying subsystem models. Independent…
We consider the problem of performing Bayesian inference for logistic regression using appropriate extensions of the ensemble Kalman filter. Two interacting particle systems are proposed that sample from an approximate posterior and prove…
A generalisation of the Lie symmetry method is applied to classify a coupled system of reaction-diffusion equations wherein the nonlinearities involve arbitrary functions in the limit case in which one equation of the pair is quasi-steady…
This paper presents a unified framework for uncertainty propagation in dynamical systems involving hybrid aleatory and epistemic uncertainties. The framework accommodates precise probabilistic, imprecise probabilistic, and non-probabilistic…
In this paper, we use the Bayesian inversion approach to study the data assimilation problem for a family of tumor growth models described by porous-medium type equations. The models contain uncertain parameters and are indexed by a…
Irregular distribution in latent space causes posterior collapse, misalignment between posterior and prior, and ill-sampling problem in Variational Autoencoders (VAEs). In this paper, we introduce a novel adaptable three-stage Uniform…
In this paper, distributed Bayesian detection problems with unknown prior probabilities of hypotheses are considered. The sensors obtain observations which are conditionally dependent across sensors and their probability density functions…
We introduce a Bayesian approach to predictive density calibration and combination that accounts for parameter uncertainty and model set incompleteness through the use of random calibration functionals and random combination weights.…
This paper addresses the problem of quantification and propagation of uncertainties associated with dependence modeling when data for characterizing probability models are limited. Practically, the system inputs are often assumed to be…
Motivated by the problem of computer-aided detection (CAD) of pulmonary nodules, we introduce methods to propagate and fuse uncertainty information in a multi-stage Bayesian convolutional neural network (CNN) architecture. The question we…