Related papers: Multilevel Bayesian Parameter Estimation in the Pr…

This study proposes a novel approach to quantifying uncertainties of constitutive relations inferred from noisy experimental data using inverse modelling. We focus on electrochemical systems in which charged species (e.g., Lithium ions) are…

The Best Estimate plus Uncertainty (BEPU) approach for nuclear systems modeling and simulation requires that the prediction uncertainty must be quantified in order to prove that the investigated design stays within acceptance criteria. A…

A critical step in data analysis for many different types of experiments is the identification of features with theoretically defined shapes in N-dimensional datasets; examples of this process include finding peaks in multi-dimensional…

Quantifying uncertainty and updating reliability are essential for ensuring the safety and performance of engineering systems. This study develops a hierarchical Bayesian modeling (HBM) framework to quantify uncertainty and update…

Real-world data contains aleatoric uncertainty - irreducible noise arising from imperfect measurements or from incomplete knowledge about the data generation process. Mean-variance estimation networks can learn this type of uncertainty but…

There are many issues that can cause problems when attempting to infer model parameters from data. Data and models are both imperfect, and as such there are multiple scenarios in which standard methods of inference will lead to misleading…

Inference of physical parameters from reference data is a well studied problem with many intricacies (inconsistent sets of data due to experimental systematic errors, approximate physical models...). The complexity is further increased when…

This paper offers a qualitative insight into the convergence of Bayesian parameter inference in a setup which mimics the modeling of the spread of a disease with associated disease measurements. Specifically, we are interested in the…

Bayesian inverse problems use observed data to update a prior probability distribution for an unknown state or parameter of a scientific system to a posterior distribution conditioned on the data. In many applications, the unknown parameter…

The objective of this work is to quantify the uncertainty in probability of failure estimates resulting from incomplete knowledge of the probability distributions for the input random variables. We propose a framework that couples the…

We consider the task of forecasting an infinite sequence of future observations based on some number of past observations, where the probability measure generating the observations is "suspected" to satisfy one or more of a set of…

Unfair predictions of machine learning (ML) models impede their broad acceptance in real-world settings. Tackling this arduous challenge first necessitates defining what it means for an ML model to be fair. This has been addressed by the ML…

Consistent experiment data are crucial to adjust parameters of physics models and to determine best estimates of observables. However, often experiment data are not consistent due to unrecognized systematic errors. Standard methods of…

Parameter estimation and inference from complex survey samples typically focuses on global model parameters whose estimators have asymptotic properties, such as from fixed effects regression models. The central challenge is to both mitigate…

Identifying and disentangling sources of predictive uncertainty is essential for trustworthy supervised learning. We argue that widely used second-order methods that disentangle aleatoric and epistemic uncertainty are fundamentally…

Diffusion models have recently driven significant breakthroughs in generative modeling. While state-of-the-art models produce high-quality samples on average, individual samples can still be low quality. Detecting such samples without human…

Neural networks make accurate predictions but often fail to provide reliable uncertainty estimates, especially under covariate distribution shifts between training and testing. To address this problem, we propose a Bayesian framework for…

In the context of industrially mass-manufactured products, quality management is based on physically inspecting a small sample from a large batch and reasoning about the batch's quality conformance. When complementing physical inspections…

We report an inconsistency found in probability theory (also referred to as measure-theoretic probability). For probability measures induced by real-valued random variables, we deduce an "equality" such that one side of the "equality" is a…

We propose a novel iterative algorithm for estimating a deterministic but unknown parameter vector in the presence of model uncertainties. This iterative algorithm is based on a system model where an overall noise term describes both, the…