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Area of Science:

  • Computational Chemistry
  • cheminformatics
  • Data Science

Background:

  • Benchmarking studies in computational chemistry rely on error statistics to evaluate method accuracy.
  • Commonly used statistics like mean signed and unsigned errors do not quantify expected prediction error amplitudes.
  • The non-normal and non-zero-centered distributions of model errors limit the inference of prediction error probabilities from standard statistics.

Purpose of the Study:

  • To address the limitations of traditional error statistics in computational chemistry benchmarking.
  • To propose and advocate for more informative error statistics for assessing prediction errors.
  • To enhance the reliability and interpretability of benchmarking and ranking studies.

Main Methods:

  • Analysis of model error distributions in computational chemistry.
  • Development and application of statistics based on the empirical cumulative distribution function of unsigned errors.
  • Evaluation of the suitability of proposed statistics for benchmarking and ranking.

Main Results:

  • Traditional error statistics (mean signed/unsigned errors) are inadequate for inferring prediction error probabilities due to non-normal error distributions.
  • Proposed statistics, including probability of error below a threshold and maximal error at a confidence level, provide better insights.
  • The statistical reliability of benchmarking statistics is dependent on the reference dataset size, necessitating the publication of standard errors.

Conclusions:

  • More informative error statistics derived from error distributions are crucial for accurate computational chemistry benchmarking.
  • The proposed statistics enable end-users to better understand and predict the amplitude of errors associated with computational methods.
  • Systematic reporting of standard errors alongside benchmarking statistics is essential for assessing their statistical reliability.