Fast matrix algebra for Bayesian model calibration

Rumsey, Kellin N.; Huerta, Gabriel

doi:10.1080/00949655.2020.1850729

Cited by 2 publications

(3 citation statements)

References 14 publications

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“…On the other hand, Kejzlar et al (2021) used an empirical Bayes approach, wherein instead of placing a prior distribution on the unknown parameters, including θ, σ 2 ε , γ, ω, μ δ , and μ f , the method estimates these parameters directly from the data. To enhance the efficiency of the MCMC methods, Rumsey and Huerta (2021) employed the eigenvalue decomposition to approximate the inverse of the covariance matrix in the likelihood (6), that is,…”

Section: Expensive Computer Simulationmentioning

confidence: 99%

“…On the other hand, Kejzlar et al (2021) used an empirical Bayes approach, wherein instead of placing a prior distribution on the unknown parameters, including

\boldsymbol{\theta}

{\sigma}_{\varepsilon}^2

\boldsymbol{\gamma}

\boldsymbol{\omega}

{\mu}_{\delta }

, and

{\mu}_f

, the method estimates these parameters directly from the data. To enhance the efficiency of the MCMC methods, Rumsey and Huerta (2021) employed the eigenvalue decomposition to approximate the inverse of the covariance matrix in the likelihood (), that is,

{\left({\tau}_{\delta }{\Phi}_{\delta}\left(\boldsymbol{\gamma} \right)+{\sigma}^2{\mathbf{I}}_n\right)}^{-1}

, which can be computed in nearly quadratic time. Furthermore, Kejzlar and Maiti (2023) used variational Bayes inference (Blei et al, 2017), an alternative Bayesian inference to MCMC, which has been widely used to approximate the posterior distribution through optimization as it tends to be faster and easier to scale to massive datasets.…”

Section: Posterior Inferencementioning

confidence: 99%

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A review on computer model calibration

Sung,

Tuo

2024

WIREs Computational Stats

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Model calibration is crucial for optimizing the performance of complex computer models across various disciplines. In the era of Industry 4.0, symbolizing rapid technological advancement through the integration of advanced digital technologies into industrial processes, model calibration plays a key role in advancing digital twin technology, ensuring alignment between digital representations and real‐world systems. This comprehensive review focuses on the Kennedy and O'Hagan (KOH) framework (Kennedy and O'Hagan, Journal of the Royal Statistical Society: Series B 2001; 63(3):425–464). In particular, we explore recent advancements addressing the challenges of the unidentifiability issue while accommodating model inadequacy within the KOH framework. In addition, we explore recent advancements in adapting the KOH framework to complex scenarios, including those involving multivariate outputs and functional calibration parameters. We also delve into experimental design strategies tailored to the unique demands of model calibration. By offering a comprehensive analysis of the KOH approach and its diverse applications, this review serves as a valuable resource for researchers and practitioners aiming to enhance the accuracy and reliability of their computer models.This article is categorized under: Statistical Models > Semiparametric Models Statistical Models > Simulation Models Statistical Models > Bayesian Models

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Section: Expensive Computer Simulationmentioning

confidence: 99%

“…On the other hand, Kejzlar et al (2021) used an empirical Bayes approach, wherein instead of placing a prior distribution on the unknown parameters, including

\boldsymbol{\theta}

{\sigma}_{\varepsilon}^2

\boldsymbol{\gamma}

\boldsymbol{\omega}

{\mu}_{\delta }

, and

{\mu}_f

{\left({\tau}_{\delta }{\Phi}_{\delta}\left(\boldsymbol{\gamma} \right)+{\sigma}^2{\mathbf{I}}_n\right)}^{-1}

Section: Posterior Inferencementioning

confidence: 99%

A review on computer model calibration

Sung,

Tuo

2024

WIREs Computational Stats

View full text Add to dashboard Cite

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“…Since

K

varies with the unknown parameters

bold-italicκ

, many cubic‐time inversions may be needed. By fixing

κ_{2}

at an empirically reasonable value, substantial speedup can be obtained in applications such as Bayesian model calibration(Rumsey & Huerta, 2021), but it remains a computational bottleneck and limits deployment of the full scale GP to problems with only a moderate number of model runs.…”

Section: Introductionmentioning

confidence: 99%

A localized ensemble of approximate Gaussian processes for fast sequential emulation

Rumsey

Huerta

Tucker

2023

Stat

Self Cite

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More attention has been given to the computational cost associated with the fitting of an emulator. Substantially less attention is given to the computational cost of using that emulator for prediction. This is primarily because the cost of fitting an emulator is usually far greater than that of obtaining a single prediction, and predictions can often be obtained in parallel. In many settings, especially those requiring Markov Chain Monte Carlo, predictions may arrive sequentially and parallelization is not possible. In this case, using an emulator procedure which can produce accurate predictions efficiently can lead to substantial time savings in practice. In this paper, we propose a global model approximate Gaussian process framework via extension of a popular local approximate Gaussian process (laGP) framework. Our proposed emulator can be viewed as a treed Gaussian process where the leaf nodes are laGP models, and the tree structure is learned greedily as a function of the prediction stream. The suggested method (called leapGP) has interpretable tuning parameters which control the time‐memory trade‐off. One reasonable choice of settings leads to an emulator with a training cost and makes predictions rapidly with an asymptotic amortized cost of .

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Fast matrix algebra for Bayesian model calibration

Cited by 2 publications

References 14 publications

A review on computer model calibration

A review on computer model calibration

A localized ensemble of approximate Gaussian processes for fast sequential emulation

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