Related papers: Goal-Oriented A-Posteriori Estimation of Model Err…

We study objective Bayesian inference for linear regression models with residual errors distributed according to the class of two-piece scale mixtures of normal distributions. These models allow for capturing departures from the usual…

We consider goal-oriented optimal design of experiments for infinite-dimensional Bayesian linear inverse problems governed by partial differential equations (PDEs). Specifically, we seek sensor placements that minimize the posterior…

In model development, model calibration and validation play complementary roles toward learning reliable models. In this article, we expand the Bayesian Validation Metric framework to a general calibration and validation framework by…

Bayesian decision theory provides an elegant framework for acting optimally under uncertainty when tractable posterior distributions are available. Modern Bayesian models, however, typically involve intractable posteriors that are…

In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…

Bayesian optimization (BO) selects evaluation points for expensive black-box objectives using Gaussian process (GP) predictive distributions. Kernel choice and hyperparameter selection can lead to miscalibrated predictive distributions and…

Bayesian optimization (BO) is a widely-used method for optimizing expensive (to evaluate) problems. At the core of most BO methods is the modeling of the objective function using a Gaussian Process (GP) whose covariance is selected from a…

This paper presents an efficient Bayesian framework for solving nonlinear, high-dimensional model calibration problems. It is based on a Variational Bayesian formulation that aims at approximating the exact posterior by means of solving an…

In this study we propose a-posteriori error estimation results to approximate the precision loss in quantities of interests computed using reduced order models. To generate the surrogate models we employ Proper Orthogonal Decomposition and…

In this work, we describe a new approach that uses variational encoder-decoder (VED) networks for efficient goal-oriented uncertainty quantification for inverse problems. Contrary to standard inverse problems, these approaches are…

Computer models, aiming at simulating a complex real system, are often calibrated in the light of data to improve performance. Standard calibration methods assume that the optimal values of calibration parameters are invariant to the model…

Autoregressive cokriging models have been widely used to emulate multiple computer models with different levels of fidelity. The dependence structures are modeled via Gaussian processes at each level of fidelity, where covariance structures…

A predictive Bayesian model selection approach is presented to discriminate coupled models used to predict an unobserved quantity of interest (QoI). The need for accurate predictions arises in a variety of critical applications such as…

Many large-scale machine learning problems involve estimating an unknown parameter $\theta_{i}$ for each of many items. For example, a key problem in sponsored search is to estimate the click through rate (CTR) of each of billions of…

Observational healthcare data offer the potential to estimate causal effects of medical products on a large scale. However, the confidence intervals and p-values produced by observational studies only account for random error and fail to…

With new advancements in technology, it is now possible to collect data for a variety of different metrics describing tumor growth, including tumor volume, composition, and vascularity, among others. For any proposed model of tumor growth…

We introduce a computational efficient data-driven framework suitable for quantifying the uncertainty in physical parameters and model formulation of computer models, represented by differential equations. We construct physics-informed…

In critical decision support systems based on medical imaging, the reliability of AI-assisted decision-making is as relevant as predictive accuracy. Although deep learning models have demonstrated significant accuracy, they frequently…

Discovery of an accurate causal Bayesian network structure from observational data can be useful in many areas of science. Often the discoveries are made under uncertainty, which can be expressed as probabilities. To guide the use of such…

This work reviews goal-oriented a posteriori error control, adaptivity and solver control for finite element approximations to boundary and initial-boundary value problems for stationary and non-stationary partial differential equations,…