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

A review on computer model calibration

“…Instead of coupling the data D s and D p to infer the posterior, they suggested first training the emulator, b f x, θ ð Þ, using the predictive mean of the GP posterior based on the simulation data D s , and then inferring the posterior as done previously by replacing f with b f . 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,…”

“…Instead of coupling the data $$$ {\mathcal{D}}^s $$$ and $$$ {\mathcal{D}}^p $$$ to infer the posterior, they suggested first training the emulator, $$$ \hat{f}\left(\mathbf{x},\boldsymbol{\theta} \right) $$$, using the predictive mean of the GP posterior based on the simulation data $$$ {\mathcal{D}}^s $$$, and then inferring the posterior as done previously by replacing $$$ f $$$ with $$$ \hat{f} $$$. 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, …”