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Seeing through noise in power laws.

Qianying Lin1,2, Mitchell Newberry3,4,5

  • 1Theoretical Biology and Biophysics, Los Alamos National Laboratory, Los Alamos, NM, USA.

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|August 29, 2023
PubMed
Summary
This summary is machine-generated.

Power law analysis is often unreliable due to data errors. Logarithmic binning improves accuracy and reliability for power law inference, enhancing statistical testing.

Keywords:
Pareto distributionextreme valuefat tailscale-freeself-similaritytail index

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Area of Science:

  • Statistical analysis
  • Natural and social sciences
  • Data science

Background:

  • Power laws are widely claimed across disciplines, but empirical evidence is often ambiguous.
  • Standard statistical methods and estimators frequently reject established power laws, leading to inconsistencies.
  • Existing methods are highly sensitive to common data imperfections like noise and censoring.

Purpose of the Study:

  • To investigate the impact of data errors on power law inference.
  • To propose and evaluate a novel method for improving the accuracy and reliability of power law analysis.
  • To address the spurious rejection of power laws and parameter estimation biases.

Main Methods:

  • Analysis of maximum-likelihood estimators and Kolmogorov-Smirnov (K-S) statistics.
  • Introduction and application of logarithmic binning with powers of lambda (λ > 1).
  • Evaluation of binning's effect on error attenuation, accuracy-precision trade-offs, and test sensitivity/specificity.

Main Results:

  • Ubiquitous data errors significantly impact standard power law estimators, causing false rejections and biased estimates.
  • Logarithmic binning effectively reduces data errors, analogous to noise averaging in other statistical domains.
  • Binning allows tuning of accuracy and precision, and can enhance the sensitivity and specificity of statistical tests.

Conclusions:

  • Logarithmic binning is a crucial and simple step for robust power law inference.
  • This method mitigates the negative effects of data errors on statistical analysis.
  • The findings explain discrepancies between theoretical power laws and empirical data.