Related papers: Bayesian Projected Calibration of Computer Models

We study system design problems stated as parameterized stochastic programs with a chance-constraint set. We adopt a Bayesian approach that requires the computation of a posterior predictive integral which is usually intractable. In…

This paper addresses the use of experimental data for calibrating a computer model and improving its predictions of the underlying physical system. A global statistical approach is proposed in which the bias between the computer model and…

Probabilistic predictions from neural networks which account for predictive uncertainty during classification is crucial in many real-world and high-impact decision making settings. However, in practice most datasets are trained on…

We tackle the problem of system identification, where we select inputs, observe the corresponding outputs from the true system, and optimize the parameters of our model to best fit the data. We propose a practical and computationally…

Dynamical system state estimation and parameter calibration problems are ubiquitous across science and engineering. Bayesian approaches to the problem are the gold standard as they allow for the quantification of uncertainties and enable…

Reliable uncertainty quantification remains a central challenge in predictive modeling. While Bayesian methods are theoretically appealing, their predictive intervals can exhibit poor frequentist calibration, particularly with small sample…

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.…

Many imaging problems require solving an inverse problem that is ill-conditioned or ill-posed. Imaging methods typically address this difficulty by regularising the estimation problem to make it well-posed. This often requires setting the…

Projected kernel calibration is a newly proposed frequentist calibration method, which is asymptotic normal and semi-parametric. Its loss function is usually referred to as the PK loss function. In this work, we prove the uniform…

Numerical simulations are widely used to predict the behavior of physical systems, with Bayesian approaches being particularly well suited for this purpose. However, experimental observations are necessary to calibrate certain simulator…

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…

In robotics, simulation has the potential to reduce design time and costs, and lead to a more robust engineered solution and a safer development process. However, the use of simulators is predicated on the availability of good models. This…

Current methods for learning graphical models with latent variables and a fixed structure estimate optimal values for the model parameters. Whereas this approach usually produces overfitting and suboptimal generalization performance,…

Experimental calibration of dynamic thermal models is required for model predictive control and characterization of building energy performance. In these applications, the uncertainty assessment of the parameter estimates is decisive; this…

In this work, a Bayesian model calibration framework is presented that utilizes goal-oriented a-posterior error estimates in quantities of interest (QoIs) for classes of high-fidelity models characterized by PDEs. It is shown that for a…

The Bayesian statistical framework provides a systematic approach to enhance the regularization model by incorporating prior information about the desired solution. For the Bayesian linear inverse problems with Gaussian noise and Gaussian…

Gaussian processes allow for flexible specification of prior assumptions of unknown dynamics in state space models. We present a procedure for efficient Bayesian learning in Gaussian process state space models, where the representation is…

This article revisits the problem of Bayesian shape-restricted inference in the light of a recently developed approximate Gaussian process that admits an equivalent formulation of the shape constraints in terms of the basis coefficients. We…

We propose Bayesian Conformal Prediction (BCP), a framework that combines Bayesian posterior predictive distributions with PAC-style conformal risk control to produce prediction sets with finite-sample coverage guarantees. Standard…

Uncertainty quantification is essential when dealing with ill-conditioned inverse problems due to the inherent nonuniqueness of the solution. Bayesian approaches allow us to determine how likely an estimation of the unknown parameters is…