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Testing Statistical Laws in Complex Systems.

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Statistical analysis of complex systems is impacted by data correlations. Accounting for these correlations reduces false law rejections and improves parameter estimates for laws like Zipf

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Area of Science:

  • Complex systems analysis
  • Statistical physics
  • Data science

Background:

  • Large datasets in complex systems often exhibit correlations.
  • Standard statistical analysis may misinterpret these correlations.
  • Established laws (e.g., Zipf's law, Gutenberg-Richter law) are susceptible to correlation biases.

Purpose of the Study:

  • To investigate the impact of correlations on statistical laws in complex systems.
  • To evaluate standard maximum-likelihood methods in the presence of correlations.
  • To propose and validate a robust method for testing statistical laws with correlated data.

Main Methods:

  • Analysis of statistical laws (e.g., Zipf's law, Gutenberg-Richter law) in complex systems.
  • Simulation and testing of standard maximum-likelihood estimation techniques.
  • Development and application of a conservative statistical testing method involving data shuffling and undersampling.

Main Results:

  • Standard methods incorrectly reject statistical laws when data contains correlations.
  • The proposed conservative method significantly reduces false rejection rates.
  • Accounting for correlations leads to more reliable parameter estimation and wider confidence intervals.

Conclusions:

  • Correlations in complex system data necessitate advanced statistical approaches.
  • The proposed method offers a more accurate way to test and validate statistical laws.
  • Improved statistical analysis enhances our understanding of complex system behaviors.