Calibration for Computer Experiments With Binary Responses and Application to Cell Adhesion Study

Abstract

Calibration refers to the estimation of unknown parameters which are present in computer experiments but not available in physical experiments. An accurate estimation of these parameters is important because it provides a scientific understanding of the underlying system which is not available in physical experiments. Most of the work in the literature is limited to the analysis of continuous responses. Motivated by a study of cell adhesion experiments, we propose a new calibration framework for binary responses. Its application to the T cell adhesion data provides insight into the unknown values of the kinetic parameters which are difficult to determine by physical experiments due to the limitation of the existing experimental techniques.

Quantifying Spatio-Temporal Boundary Condition Uncertainty for the North American Deglaciation

“…We have spatial binary observations for the ice extent, z b , at certain time points, whereas Glimmer's output is ice thickness. (binary output, binary observations) and Chang et al (2019) (binary and thickness output, thickness observations) provide extensions to Bayesian calibration problems with binary data, and Sung et al (2020) provide an alternative calibration approach for univariate binary output. Our application is slightly different, in that we have thickness output to be compared to binary observations, and rather than applying the binary-only method , we allow the thickness to be incorporated into the emulation and calibration process, prior to comparison to the observations.…”

Efficient calibration for imperfect epidemic models with applications to the analysis of COVID-19

“…The proposed method is applied to estimate unknown parameters in compartmental models for the analysis of COVID-19 pandemic. According to the epidemiology literature, the SEIR model, which consists of four compartments, S usceptible-E xposed-I nfectious-Recovered, is widely recommended for COVID-19 simulations because it accounts for the incubation period through the exposed compartment (Wu et al, 2020;Carcione et al, 2020;Mwalili et al, 2020;He et al, 2020;Annas et al, 2020). We focus on two types of SEIR simulators:…”

“…The proof is developed along the lines described in Theorem 1 of and Theorem 3.1 of Sung et al (2020). We first prove the consistency, θn…”

“…It is worth noting that there are extensive studies and applications of calibration by Bayesian procedures (Diekmann et al, 2013;Farah et al, 2014;Wang et al, 2020;Wu et al, 2020). However, without taking the model imperfection into account in the conventional Bayesian framework, the theoretical justification for the parameter estimation with imperfect simulators are not fully developed.…”

Calibration of inexact computer models with heteroscedastic errors

“…This process is called calibration, and it is of great importance for computer modelers because it not only improves the model prediction, but the estimated value of the calibration parameters also provides some scientific insight which can help modelers better understand the system. For example, the parameters in the cell adhesion study of Sung et al (2019) include kinetic rates and their estimated values provide the information of molecular interactions in the biological system. An improved understanding of a biological system is also vital towards efforts to re-engineer improvements to the system of interest.…”