Related papers: Uncertainty quantification for Markov Random Field…
We introduce a framework for uncertainty estimation that both describes and extends many existing methods. We consider typical hyperparameters involved in classical training as random variables and marginalise them out to capture various…
In hydrology, modeling streamflow remains a challenging task due to the limited availability of basin characteristics information such as soil geology and geomorphology. These characteristics may be noisy due to measurement errors or may be…
Scientists use mathematical modelling to understand and predict the properties of complex physical systems. In highly parameterised models there often exist relationships between parameters over which model predictions are identical, or…
I develop Macroeconomic Random Forest (MRF), an algorithm adapting the canonical Machine Learning (ML) tool to flexibly model evolving parameters in a linear macro equation. Its main output, Generalized Time-Varying Parameters (GTVPs), is a…
Statistical models are inherently uncertain. Quantifying or at least upper-bounding their uncertainties is vital for safety-critical systems such as autonomous vehicles. While standard neural networks do not report this information, several…
Contour maps are widely used to display estimates of spatial fields. Instead of showing the estimated field, a contour map only shows a fixed number of contour lines for different levels. However, despite the ubiquitous use of these maps,…
The design of next-generation alloys through the Integrated Computational Materials Engineering (ICME) approach relies on multi-scale computer simulations to provide thermodynamic properties when experiments are difficult to conduct.…
Parameter inference and uncertainty quantification are important steps when relating mathematical models to real-world observations, and when estimating uncertainty in model predictions. However, methods for doing this can be…
Mathematical models are essential tools to study how the cardiovascular system maintains homeostasis. The utility of such models is limited by the accuracy of their predictions, which can be determined by uncertainty quantification (UQ). A…
Purpose: The purpose of this study is to address the lack of uncertainty quantification in numerical hemolysis models, which are critical for medical device evaluations. Specifically, we aim to incorporate experimental variability into…
We develop a new Bayesian model for non-rigid registration of three-dimensional medical images, with a focus on uncertainty quantification. Probabilistic registration of large images with calibrated uncertainty estimates is difficult for…
Constructing probability densities for inference in high-dimensional spectral data is often intractable. In this work, we use normalizing flows on structured spectral latent spaces to estimate such densities, enabling downstream inference…
Uncertainty quantification (UQ) includes the characterization, integration, and propagation of uncertainties that result from stochastic variations and a lack of knowledge or data in the natural world. Monte Carlo (MC) method is a…
Belief Propagation (BP) is a widely used approximation for exact probabilistic inference in graphical models, such as Markov Random Fields (MRFs). In graphs with cycles, however, no exact convergence guarantees for BP are known, in general.…
Markov chain geostatistics is a methodology for simulating categorical fields. Its fundamental model for conditional simulation is the Markov chain random field (MCRF) model, and its basic spatial correlation measure is the transiogram.…
Uncertainty quantification is an important and challenging problem in deep learning. Previous methods rely on dropout layers which are not present in modern deep architectures or batch normalization which is sensitive to batch sizes. In…
Turbulent dynamical systems characterized by both a high-dimensional phase space and a large number of instabilities are ubiquitous among many complex systems in science and engineering. The existence of a strange attractor in the turbulent…
Uncertainty quantification for Particle Image Velocimetry (PIV) is critical for comparing flow fields with Computational Fluid Dynamics (CFD) results, and model design and validation. However, PIV features a complex measurement chain with…
We present a simple comparative framework for testing and developing uncertainty modeling in uncertain marching cubes implementations. The selection of a model to represent the probability distribution of uncertain values directly…
The uncertainty principle is one of the fundamental features of quantum mechanics and plays an essential role in quantum information theory. We study uncertainty relations based on variance for arbitrary finite $N$ quantum observables. We…