Calibration of Inexact Computer Models with Heteroscedastic Errors

A review on computer model calibration

“…When dealing with replicated physical experiments, it is not uncommon to encounter heteroscedasticity. In response to this challenge, Sung et al (2022) have introduced a new statistical model that facilitates the estimation of calibration parameters and the generation of predictions in the presence of heteroscedasticity. Specifically, they consider an inputdependent error model:…”

“…When dealing with replicated physical experiments, it is not uncommon to encounter heteroscedasticity. In response to this challenge, Sung et al (2022) have introduced a new statistical model that facilitates the estimation of calibration parameters and the generation of predictions in the presence of heteroscedasticity. Specifically, they consider an input‐dependent error model: $$$$ {y}_i^p=f\left({\mathbf{x}}_i^p,\boldsymbol{\theta} \right)+\delta \left({\mathbf{x}}_i^p\right)+\upvarepsilon \left({\mathbf{x}}_i^p\right), $$$$ where the measurement error follows an independent normal distribution with heteroscedastic variance, that is, $$$ \upvarepsilon \left(\mathbf{x}\right)\sim \mathcal{N}\left(0,r\left(\mathbf{x}\right)\right) $$$.…”

“…In the case of replication, they utilize a latent GP prior to model $$$ r\left(\mathbf{x}\right) $$$, drawing upon the concepts proposed by Goldberg et al (1998) and Binois et al (2018). The R package HetCalibrate (Sung, 2020) is available on an open repository for implementing this approach.…”

“…Through calibration, researchers can fine‐tune these models to accurately capture the intricacies of the systems they represent. Notably, the calibration process plays a pivotal role in fields such as nuclear physics (Higdon et al, 2015; Kejzlar et al, 2020; King et al, 2019; Pratola & Higdon, 2016), biology (Henderson et al, 2009; Sung et al, 2020, 2022), environmental sciences (Cheng et al, 2021; Larssen et al, 2006), climatology (Forest et al, 2008; Higdon et al, 2013; Konomi et al, 2017; Lee et al, 2020; Salter et al, 2019), hydrology (Goh et al, 2013; Gramacy et al, 2015; Pratola & Chkrebtii, 2018), manufacturing (Wang et al, 2020), epidemiology (Farah et al, 2014; Sung & Hung, 2024; Wang et al, 2022), health care (Oakley & Youngman, 2017), mechanical engineering (Gattiker et al, 2006), aerospace (Allaire et al, 2012; Huang et al, 2020; Zhou et al, 2023), material science (Generale et al, 2022), transfer learning (Liyanage et al, 2022), robotics (Liu & Negrut, 2021), and digital twins (Kenett & Bortman, 2022; Thelen et al, 2022, 2023), where accurate predictions are essential for informed decision‐making.…”