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Convergence of large-deviation estimators.

Christian M Rohwer1,2,3, Florian Angeletti4, Hugo Touchette3,4

  • 1Max-Planck-Institut für Intelligente Systeme, Heisenbergstraße 3, D-70569 Stuttgart, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 15, 2015
PubMed
Summary

This study establishes a framework for accurately estimating large-deviation functions by analyzing statistical estimator convergence. It provides conditions for reliable estimation from simulation and experimental data.

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Area of Science:

  • Statistical physics
  • Stochastic systems analysis
  • Computational modeling

Background:

  • Estimating large-deviation functions is crucial for understanding system fluctuations.
  • Existing methods face challenges with statistical errors and convergence.
  • Reported "phase transitions" in free energy estimators lack a unified explanation.

Purpose of the Study:

  • To develop a general framework for reliable estimation of large-deviation functions.
  • To provide conditions for the convergence of statistical estimators based on sample size.
  • To clarify the nature of statistical errors in different convergence regions.

Main Methods:

  • Analysis of statistical estimator convergence with increasing sample size.
  • Investigation of conditions based on the boundedness of sampled quantities.
  • Examination of statistical error definitions across convergence regions.

Main Results:

  • Conditions for the convergence of statistical estimators are established.
  • The influence of sample size on estimator accuracy is quantified.
  • A unified explanation for observed "phase transitions" in free energy estimators is provided.

Conclusions:

  • The study offers a robust framework for estimating large-deviation functions from diverse data sources.
  • Reliable estimation is achievable by identifying appropriate parameter regions.
  • Understanding estimator convergence is key to accurate analysis of stochastic systems.