Calibrating Non-Identifiable High-Dimensional Simulation Models: A Framework via Eligibility Set
针对高维且不可识别的随机仿真模型，提出一种基于合格集的校准框架，通过特征提取与聚合方法构建集合估计，提供严格的频率统计保证，并在限价订单簿市场模拟器ABIDES上验证。
Stochastic simulation aims to compute output performance for complex models that lack analytical tractability. To ensure accurate prediction, the model needs to be calibrated and validated against real data. Conventional methods approach these tasks by assessing the model-data match via simple hypothesis tests or distance minimization in an ad hoc fashion, but they can encounter challenges arising from non-identifiability and high dimensionality. In this article, we investigate a framework to develop calibration schemes that satisfies rigorous frequentist statistical guarantees, via a basic notion that we call eligibility set designed to bypass non-identifiability via a set-based estimation. We investigate a feature extraction-then-aggregation approach to construct these sets that target at multivariate outputs. We demonstrate our methodology on several numerical examples, including an application to calibration of a limit order book market simulator (ABIDES).