A Parameter Estimation Method Using Linear Response Statistics
It addresses the problem of parameter estimation for stochastic dynamical systems where the goal is to predict both equilibrium behavior and response to perturbations, which is important for modeling complex systems.
This paper proposes a parameter estimation method for Itô diffusions that ensures the model matches equilibrium statistics and sensitivities to disturbances, using linear response statistics from fluctuation-dissipation theory. The method is shown to be consistent, recovering true parameters in test problems.
This paper presents a new parameter estimation method for Itô diffusions such that the resulting model predicts the equilibrium statistics as well as the sensitivities of the underlying system to external disturbances. Our formulation does not require the knowledge of the underlying system, however we assume that the linear response statistics can be computed via the fluctuation-dissipation theory. The main idea is to fit the model to a finite set of "essential" statistics that is sufficient to approximate the linear response operators. In a series of test problems, we will show the consistency of the proposed method in the sense that if we apply it to estimate the parameters in the underlying model, then we must obtain the true parameters.