Abstract
Parameters of differential equations are essential to characterize intrinsic behaviours of dynamic systems. Numerous methods for estimating parameters in dynamic systems are computationally and/or statistically inadequate, especially for complex systems with general-order differential operators, such as motion dynamics. This article presents Green’s matching, a computationally tractable and statistically efficient two-step method, which only needs to approximate trajectories in dynamic systems but not their derivatives due to the inverse of differential operators by Green’s function. This yields a statistically optimal guarantee for parameter estimation in general-order equations, a feature not shared by existing methods, and provides an efficient framework for broad statistical inferences in complex dynamic systems.
Jianbin Tan
Ph.D. of Statistics
I’m a Ph.D. candidate working with Prof. Hui Huang in the School of Mathematics, SYSU, since 2019, and also a visiting student working with Prof. Xueqin Wang in the School of Management, USTC, from 2021 to 2022. I’m currently interested in statistical modeling and inference of trajectory data, such as dynamic data or functional data from dependent processes in physics, biology, social networks, and so on. I prefer the empirical Bayesian paradigm for encoding the mysteries among trajectories, thereby promoting scientific discovery and insightful understanding in different domains.
