Green’s matching: an efficient approach to parameter estimation in complex dynamic systems
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<jats:title>Abstract</jats:title> <jats:p>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.</jats:p>
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Tan, Jianbin, Guoyu Zhang, Xueqin Wang, Hui Huang and Fang Yao (n.d.). Green’s matching: an efficient approach to parameter estimation in complex dynamic systems. Journal of the Royal Statistical Society Series B: Statistical Methodology. 10.1093/jrsssb/qkae031 Retrieved from https://hdl.handle.net/10161/30492.
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Jianbin Tan
My research interests lie in statistical learning for data with dynamic-, longitudinal-, or trajectory- based structures. Such data often exhibit complicated intrinsic mechanisms, dependencies, and heterogeneity, as well as challenges such as noise, irregular sampling, and high- or even infinite-dimensionality. To address these, I focus on developing new methodologies for statistical learning of functions, differential equations, and operators, supporting effective analysis in biology, health, epidemiology, and environmental science.
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