A parameter estimation method using linear response statistics

Numerical scheme

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

This paper presents a numerical method to implement the parameter estimation method using response statistics that was recently formulated by the authors. The proposed approach formulates the parameter estimation problem of Itô drift diffusions as a nonlinear least-squares problem. To avoid solving the model repeatedly when using an iterative scheme in solving the resulting least-squares problems, a polynomial surrogate model is employed on appropriate response statistics with smooth dependence on the parameters. The existence of minimizers of the approximate polynomial least-squares problems that converge to the solution of the true least square problem is established under appropriate regularity assumption of the essential statistics as functions of parameters. Numerical implementation of the proposed method is conducted on two prototypical examples that belong to classes of models with a wide range of applications, including the Langevin dynamics and the stochastically forced gradient flows. Several important practical issues, such as the selection of the appropriate response operator to ensure the identifiability of the parameters and the reduction of the parameter space, are discussed. From the numerical experiments, it is found that the proposed approach is superior compared to the conventional approach that uses equilibrium statistics to determine the parameters.

Original languageEnglish (US)
Article number033101
JournalChaos
Volume29
Issue number3
DOIs
StatePublished - Mar 1 2019

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Linear Response
Parameter estimation
Numerical Scheme
Parameter Estimation
Least Squares Problem
Statistics
statistics
Nonlinear Least Squares Problem
Langevin Dynamics
Drift-diffusion
Surrogate Model
Polynomial Model
Gradient Flow
Identifiability
Iterative Scheme
Minimizer
polynomials
Parameter Space
Numerical methods
Regularity

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

Cite this

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A parameter estimation method using linear response statistics : Numerical scheme. / Zhang, He; Li, Xiantao; Harlim, John.

In: Chaos, Vol. 29, No. 3, 033101, 01.03.2019.

Research output: Contribution to journalArticle

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