A Parameter Estimation Method Using Linear Response Statistics

TL;DR

This paper introduces a novel parameter estimation technique for Itô diffusions that leverages linear response statistics to accurately predict equilibrium behaviors and sensitivities without prior knowledge of the system.

Contribution

The method uniquely estimates parameters using essential linear response statistics, ensuring consistency and applicability without needing the underlying system details.

Findings

Method accurately recovers true parameters in test problems.

Predicts equilibrium statistics and sensitivities effectively.

Demonstrates consistency of the estimation approach.

Abstract

This paper presents a new parameter estimation method for It\^{o} 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.