A model calibration procedure for count response

Abstract

In recent years, there are numerous articles about computer model calibration. But these articles mainly focus on continuous output variables for the convenience of the derivation. However, there are some other types of output data in the application area, such as binary data and count data, the former of which has been investigated very well in the area of computer model calibration and applied to cell adhesion study successfully. Inspired by the existing methods for binary data, we propose a model calibration procedure for count response, and derive the consistency and asymptotic normality of the proposed estimator of the calibration parameters by the theory of empirical process. Some simulations are conducted to verify the good performance of the proposed method.

Keywords:

• Count data
• Poisson distribution
• penalized maximal likelihood
• uncertainty quantification
• empirical process

Acknowledgments

We thank the editor-in-chief and two anonymous reviewers for their valuable comments, which led to significant improvements of the earlier version of this paper.

Additional information

Funding

This work was supported by Science Challenge Project, No. TZ2018001.