Calibrating Input Parameters via Eligibility Sets

Abstract

Reliable simulation analysis requires accurately calibrating input model parameters. While there has been a sizable literature on parameter calibration that utilizes directly observed data, much less attention has been paid to the situation where only output-level data are available to justify input parameter choices. This latter problem, which is known as the inverse problem and relates to the model validation literature, involves several new challenges, one of which is the non-identifiability issue. In this paper we introduce the concept of eligibility set to bypass non-identifiability, by relaxing the need of consistent estimation to obtaining bounds on the input parameter values. We reason this concept from the worst-case notion in robust optimization, and demonstrate how to compute eligibility set via empirical matching between the simulated and the real outputs. We substantiate our procedure with theoretical error analysis and validate its effectiveness via numerical experiments.