# Bayesian Projected Calibration of Computer Models

@article{Xie2018BayesianPC, title={Bayesian Projected Calibration of Computer Models}, author={Fangzheng Xie and Yanxun Xu}, journal={Journal of the American Statistical Association}, year={2018}, volume={116}, pages={1965 - 1982} }

Abstract We develop a Bayesian approach called the Bayesian projected calibration to address the problem of calibrating an imperfect computer model using observational data from an unknown complex physical system. The calibration parameter and the physical system are parameterized in an identifiable fashion via the L 2-projection. The physical system is imposed a Gaussian process prior distribution, which naturally induces a prior distribution on the calibration parameter through the L 2…

## 23 Citations

### General Bayesian L2 calibration of mathematical models

- Computer Science
- 2021

Methodology is proposed for the general Bayesian calibration of mathematical models where the resulting posterior distributions estimate the values of the parameters that minimize the L 2 norm of the diﬀerence between the mathematical model and true physical system.

### Variational inference with vine copulas: an efficient approach for Bayesian computer model calibration

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A pairwise decomposition of the data likelihood using vine copulas that separate the information on dependence structure in data from their marginal distributions leads to computationally efficient gradient estimates that are unbiased and thus scalable calibration of computer models with Gaussian processes.

### A fast and calibrated computer model emulator: an empirical Bayes approach

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An empirical Bayes approach to predictions of physical quantities using a computer model, where it is assumed that the computer model under consideration needs to be calibrated and is computationally expensive, to allow for closed-form and easy-to-compute predictions given by a conditional distribution induced by the Gaussian processes.

### Fast Calibration for Computer Models with Massive Physical Observations

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- 2022

Computer model calibration is a crucial step in building a reliable computer model. In the face of massive physical observations, a fast estimation for the calibration parameters is urgently needed.…

### A Theoretical Framework of the Scaled Gaussian Stochastic Process in Prediction and Calibration

- Computer ScienceSIAM/ASA J. Uncertain. Quantification
- 2022

The explicit connection between Gaussian stochastic process (GaSP) and S-GaSP is established through the orthogonal series representation, and the predictive mean estimator in the S- GaSP calibration model converges to the reality at the same rate as the GaSP with a suitable choice of the regularization and scaling parameters.

### Calibration of computer models with heteroscedastic measurement errors

- Computer Science
- 2019

A new calibration method is proposed for the physical data with heteroscedastic measurement errors of plant relative growth rates where replicates are available and this approach can be used to produce more statistically robust conclusions from computer models of biology and biochemistry in general.

### Physical Parameter Calibration

- Mathematics
- 2022

Computer simulation models are widely used to study complex physical systems. A related fundamental topic is the inverse problem, also called calibration, which aims at learning about the values of…

### Bayesian Decision-Theoretic Design of Experiments Under an Alternative Model

- Computer ScienceBayesian Analysis
- 2021

An extended framework is proposed whereby expectation of the loss is taken with respect to a joint distribution implied by an alternative statistical model, and an asymptotic approximation to the resulting expected loss is developed to aid in exploring the framework.

### Calibration of Inexact Computer Models with Heteroscedastic Errors

- MathematicsSIAM/ASA Journal on Uncertainty Quantification
- 2022

Computer models are commonly used to represent a wide range of real systems, but they often involve some unknown parameters. Estimating the parameters by collecting physical data becomes essential in…

### Penalized Projected Kernel Calibration for Computer Models

- Computer ScienceSIAM/ASA Journal on Uncertainty Quantification
- 2022

It is proved that when the sample size is large, it is extremely hard for the projected kernel calibration to identify the global minimum of the L 2 loss, i.e. the optimal value of the calibration parameters, and a frequentist method, which is asymptotic normal and semi-parametric, is suggested and analyzed in detail.

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