Objective Bayesian Analysis of a Cokriging Model for Hierarchical Multifidelity Codes

  title={Objective Bayesian Analysis of a Cokriging Model for Hierarchical Multifidelity Codes},
  author={Pulong Ma},
  journal={SIAM/ASA J. Uncertain. Quantification},
  • P. Ma
  • Published 22 October 2019
  • Computer Science
  • SIAM/ASA J. Uncertain. Quantification
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 are often parameterized up to a few parameters. The predictive distributions typically require intensive Monte Carlo approximations in previous works. This article derives new closed-form formulas to compute the means and variances of predictive… 

Figures and Tables from this paper

Beyond Matérn: On A Class of Interpretable Confluent Hypergeometric Covariance Functions
  • P. Ma, A. Bhadra
  • Mathematics
    Journal of the American Statistical Association
  • 2022
The Matérn covariance function is a popular choice for prediction in spatial statistics and uncertainty quantification literature. A key benefit of the Matérn class is that it is possible to get
Multifidelity computer model emulation with high‐dimensional output: An application to storm surge
A parallel partial autoregressive cokriging model to predict highly-accurate storm surges in a computationally efficient way over a large spatial domain is proposed and has the capability of predicting storm surges as accurately as a high-fidelity computer model given any storm characteristics.
A graphical multi-fidelity Gaussian process model, with application to emulation of expensive computer simulations
A new Graphical Multi-fidelity Gaussian process (GMGP) model is proposed, which has desirable modeling traits via two Markov properties, and admits a scalable formulation for recursively computing the posterior predictive distribution along sub-graphs.
Multi-fidelity surrogate modeling for time-series outputs
The resulting surrogate model taking into account the uncertainty in the basis construction is shown to have better performance in terms of prediction errors and uncertainty quantification than standard dimension reduction techniques.
Kriging: Beyond Mat\'ern.
The Matern covariance function is a popular choice for prediction in spatial statistics and uncertainty quantification literature. A key benefit of the Matern class is that it is possible to get


Bayesian Analysis of Hierarchical Multifidelity Codes
  • L. L. Gratiet
  • Computer Science
    SIAM/ASA J. Uncertain. Quantification
  • 2013
A new approach to estimating the model parameters which provides a closed form expression for an important parameter of the model (the scale factor), a reduction of the numerical complexity by simplifying the covariance matrix inversion, and a new Bayesian modeling that gives an explicit representation of the joint distribution of the parameters and that is not computationally expensive.
Objective Bayesian Analysis of Spatially Correlated Data
Spatially varying phenomena are often modeled using Gaussian random fields, specified by their mean function and covariance function. The spatial correlation structure of these models is commonly
Robust Gaussian stochastic process emulation
We consider estimation of the parameters of a Gaussian Stochastic Process (GaSP), in the context of emulation (approximation) of computer models for which the outcomes are real-valued scalars. The
It is proved that the predictive mean and the variance of the presented approach are identical to the ones of the original co-kriging model, and the proposed approach has a reduced computational complexity compared to the previous one.
Jointly Robust Prior for Gaussian Stochastic Process in Emulation, Calibration and Variable Selection
  • Mengyang Gu
  • Mathematics, Computer Science
    Bayesian Analysis
  • 2019
This work establishes the posterior propriety for a large class of priors in calibration, including the reference prior and jointly robust prior in general scenarios, but the jointly robustPrior is preferred because the calibrated mathematical model typically predicts the reality well.
Bayesian design and analysis of computer experiments: Use of derivatives in surface prediction
This article is concerned with the problem of predicting a deterministic response function yo over a multidimensional domain T, given values of yo and all of its first derivatives at a set of design
Default priors for Gaussian processes
The Jeffreys-rule, independence Jeffreys and reference priors are derived, and it is proved that the resulting posterior distributions are proper under a quite general set of conditions.
Overall Objective Priors
This paper considers three methods for selecting a single objective prior and study, in a variety of problems including the multinomial problem, whether or not the resulting prior is a reasonable overall prior.
Sensitivity/uncertainty analysis of a borehole scenario comparing Latin Hypercube Sampling and deterministic sensitivity approaches
A computer code was used to study steady-state flow for a hypothetical borehole scenario. The model consists of three coupled equations with only eight parameters and three dependent variables. This
Propriety of the reference posterior distribution in Gaussian Process regression
In a seminal article, Berger, De Oliveira and Sans\'o (2001) compare several objective prior distributions for the parameters of Gaussian Process regression models with isotropic correlation kernel.