Optimal Simulator Selection

Abstract

Computer simulators are widely used for the study of complex systems. In many applications, there are multiple simulators available with different scientific interpretations of the underlying mechanism, and the goal is to identify an optimal simulator based on the observed physical experiments. To achieve the goal, we propose a selection criterion based on leave-one-out cross-validation. This criterion consists of a goodness-of-fit measure and a generalized degrees of freedom penalizing the simulator sensitivity to perturbations in the physical observations. Asymptotic properties of the selected optimal simulator are discussed. It is shown that the proposed procedure includes a conventional calibration method as a special case. The finite sample performance of the proposed procedure is demonstrated through numerical examples. In the application of cell biology, an optimal simulator is selected, which can shed light on the T cell recognition mechanism in the human immune system. Supplementary materials for this article are available online.

Keywords:

• Calibration
• Computer experiment
• Cross-validation
• Emulation
• Generalized degrees of freedom

Supplementary Materials

The online supplemental material contains more technical details of this paper, including the assumptions used in Theorems 3.3 and 3.4, and the detailed proofs of the lemma, proposition, and theorems.

Acknowledgment

The authors acknowledge the support from the National Science Foundation (DMS 1660504, 1914632, and 1660477).

Additional information

Funding

Wu’s work is supported by NSF grants DMS 1660504 and 1914632, and Hung’s work is supported by NSF grants DMS 1660477.