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Likelihood-free Bayesian inference algorithms are popular methods for calibrating the parameters of complex, stochastic models, required when the likelihood of the observed data is intractable. These algorithms characteristically rely…

Computation · Statistics 2021-12-23 Thomas P Prescott , David J Warne , Ruth E Baker

Contemporary sample size calculations for external validation of risk prediction models require users to specify fixed values of assumed model performance metrics alongside target precision levels (e.g., 95% CI widths). However, due to the…

Applications · Statistics 2026-02-13 Mohsen Sadatsafavi , Paul Gustafson , Solmaz Setayeshgar , Laure Wynants , Richard D Riley

This study aims to investigate the utilization of Bayesian techniques for the calibration of micro-electro-mechanical systems (MEMS) accelerometers. These devices have garnered substantial interest in various practical applications and…

Signal Processing · Electrical Eng. & Systems 2023-06-13 Oliver Dürr , Po-Yu Fan , Zong-Xian Yin

We present a hybrid a-priori/a-posteriori goal oriented error estimator for a combination of dynamic iteration-based solution of ordinary differential equations discretized by finite elements. Our novel error estimator combines estimates…

Numerical Analysis · Mathematics 2026-02-13 Erik Weyl , Andreas Bartel , Manuel Schaller

There has been an intense development of Bayes graphical model estimation approaches over the past decade - however, most of the existing methods are restricted to moderate dimensions. We propose a novel approach suitable for high…

Methodology · Statistics 2013-08-20 Suprateek Kundu , Veera Baladandayuthapani , Bani K. Mallick

Uncertainty quantification in PDE inverse problems is essential in many applications. Scientific machine learning and AI enable data-driven learning of model components while preserving physical structure, and provide the scalability and…

Machine Learning · Computer Science 2026-01-12 Ray Zirui Zhang , Christopher E. Miles , Xiaohui Xie , John S. Lowengrub

When used in complex engineered systems, such as communication networks, artificial intelligence (AI) models should be not only as accurate as possible, but also well calibrated. A well-calibrated AI model is one that can reliably quantify…

Machine Learning · Computer Science 2022-12-16 Kfir M. Cohen , Sangwoo Park , Osvaldo Simeone , Shlomo Shamai

Computer models are widely used in science and engineering to simulate complex systems. However, these models are affected by several sources of uncertainty, which may limit their use for decision making in risk management. We present a…

Computation · Statistics 2026-03-17 Oumar Baldé , Guillaume Damblin , Amandine Marrel , Antoine Bouloré , Loïc Giraldi

In this article, goal-oriented a posteriori error estimation for the biharmonic plate bending problem is considered. The error for approximation of goal functional is represented by an estimator which combines dual-weighted residual method…

Numerical Analysis · Mathematics 2021-07-15 Gouranga Mallik

In the present work, a rate-dependent cohesive zone model for the fracture of polymeric interfaces is presented. Inverse calibration of parameters for such complex models through trial and error is computationally tedious due to the large…

Computational Engineering, Finance, and Science · Computer Science 2023-11-15 Ponkrshnan Thiagarajan , Trisha Sain , Susanta Ghosh

Inverse problems can be described as limited-data problems in which the signal of interest cannot be observed directly. A physics-based forward model that relates the signal with the observations is typically needed. Unfortunately, unknown…

Signal Processing · Electrical Eng. & Systems 2025-07-08 Alexandra Koulouri , Ville Rimpilainen

Solutions to inverse problems that are ill-conditioned or ill-posed may have significant intrinsic uncertainty. Unfortunately, analysing and quantifying this uncertainty is very challenging, particularly in high-dimensional problems. As a…

Methodology · Statistics 2016-07-12 Marcelo Pereyra

A common goal throughout science and engineering is to solve optimization problems constrained by computational models. However, in many cases a high-fidelity numerical emulation of systems cannot be optimized due to code complexity and…

Numerical Analysis · Mathematics 2023-05-31 Joseph Hart , Bart van Bloemen Waanders

We consider optimal experimental design (OED) for Bayesian nonlinear inverse problems governed by partial differential equations (PDEs) under model uncertainty. Specifically, we consider inverse problems in which, in addition to the…

Numerical Analysis · Mathematics 2024-07-03 Alen Alexanderian , Ruanui Nicholson , Noemi Petra

Deep learning has shown successful application in visual recognition and certain artificial intelligence tasks. Deep learning is also considered as a powerful tool with high flexibility to approximate functions. In the present work,…

Machine Learning · Computer Science 2021-12-23 Ayan Chakraborty , Thomas Wick , Xiaoying Zhuang , Timon Rabczuk

Bayesian calibration of black-box computer models offers an established framework to obtain a posterior distribution over model parameters. Traditional Bayesian calibration involves the emulation of the computer model and an additive model…

Machine Learning · Statistics 2018-10-30 Sébastien Marmin , Maurizio Filippone

Identifying parameters of computational models from experimental data, or model calibration, is fundamental for assessing and improving the predictability and reliability of computer simulations. In this work, we propose a method for…

Computational Physics · Physics 2023-08-07 Lianghao Cao , Keyi Wu , J. Tinsley Oden , Peng Chen , Omar Ghattas

This paper presents an a-posteriori goal-oriented error analysis for a numerical approximation of the steady Boltzmann equation based on a moment-system approximation in velocity dependence and a discontinuous Galerkin finite-element (DGFE)…

Numerical Analysis · Mathematics 2017-10-11 M. R. A. Abdelmalik , E. H. van Brummelen

In Generalised Bayesian Inference (GBI), the learning rate and hyperparameters of the loss must be estimated. These inference-hyperparameters can't be estimated jointly with the other parameters, from the data, by giving them a prior.…

Methodology · Statistics 2026-05-18 Jeong Eun Lee , Sitong Liu , Geoff K. Nicholls

Multifidelity methods are widely used for estimating quantities of interest (QoI) in computational science by employing numerical simulations of differing costs and accuracies. Many methods approximate numerical-valued statistics that…

Computation · Statistics 2022-12-02 Yiming Xu , Akil Narayan