Related papers: Contributed Discussion to Bayesian Solution Uncert…
Hyper-differential sensitivity analysis with respect to model discrepancy was recently developed to enable uncertainty quantification for optimization problems. The approach consists of two primary steps: (i) Bayesian calibration of the…
This paper discuses multiple Bayesian networks representation paradigms for encoding asymmetric independence assertions. We offer three contributions: (1) an inference mechanism that makes explicit use of asymmetric independence to speed up…
We discuss the differential equation method for establishing dynamic concentration of discrete random processes. We present several relatively simple examples of it and aim to make the method understandable to the unfamiliar reader who has…
The emergent field of probabilistic numerics has thus far lacked clear statistical principals. This paper establishes Bayesian probabilistic numerical methods as those which can be cast as solutions to certain inverse problems within the…
Stochastic diffusion equations are crucial for modeling a range of physical phenomena influenced by uncertainties. We introduce the generalized finite difference method for solving these equations. Then, we examine its consistency,…
In Bayesian inference, an unknown measurement uncertainty is often quantified in terms of a Gamma distributed precision parameter, which is impractical when prior information on the standard deviation of the measurement uncertainty shall be…
There are essentially three kinds of approaches to Uncertainty Quantification (UQ): (A) robust optimization, (B) Bayesian, (C) decision theory. Although (A) is robust, it is unfavorable with respect to accuracy and data assimilation. (B)…
We introduce implicit Bayesian neural networks, a simple and scalable approach for uncertainty representation in deep learning. Standard Bayesian approach to deep learning requires the impractical inference of the posterior distribution…
The accessibility of spatially distributed data, enabled by affordable sensors, field, and numerical experiments, has facilitated the development of data-driven solutions for scientific problems, including climate change, weather…
In this work, we propose differentially private methods for hypothesis testing, model averaging, and model selection for normal linear models. We consider Bayesian methods based on mixtures of $g$-priors and non-Bayesian methods based on…
We propose a general method to carry out a valid Bayesian analysis of a finite-dimensional `targeted' parameter in the presence of a finite-dimensional nuisance parameter. We apply our methods to causal inference based on estimating…
Nonlinear dynamics are ubiquitous in science and engineering applications, but the physics of most complex systems is far from being fully understood. Discovering interpretable governing equations from measurement data can help us…
Based the homogeneous balance method, a general method is suggested to obtain several kinds of exact solutions for some kinds of nonlinear equations. The validity and reliability of the method are tested by applying it to the Bousseneq…
Uncertainty quantification for image data is dominated by complex deep learning methods, yet the field lacks an interpretable, mathematically grounded baseline. We propose Bayesian scattering to fill this gap, serving as a first-step…
Uncertainty Quantification (UQ) is essential in probabilistic machine learning models, particularly for assessing the reliability of predictions. In this paper, we present a systematic framework for estimating both epistemic and aleatoric…
Bayesian optimization is a coherent, ubiquitous approach to decision-making under uncertainty, with applications including multi-arm bandits, active learning, and black-box optimization. Bayesian optimization selects decisions (i.e.…
A reliable modeling of uncertain evidence in Bayesian networks based on a set-valued quantification is proposed. Both soft and virtual evidences are considered. We show that evidence propagation in this setup can be reduced to standard…
Uncertainty quantification (UQ) plays a pivotal role in reduction of uncertainties during both optimization and decision making processes. It can be applied to solve a variety of real-world applications in science and engineering. Bayesian…
This paper offers a comprehensive introduction to Bayesian inference, combining historical context, theoretical foundations, and core analytical examples. Beginning with Bayes' theorem and the philosophical distinctions between Bayesian and…
We consider the problem of performing Bayesian inference in probabilistic models where observations are accompanied by uncertainty, referred to as "uncertain evidence." We explore how to interpret uncertain evidence, and by extension the…