Cumulative Distribution Function

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Andreas Savin - One of the best experts on this subject based on the ideXlab platform.

  • probabilistic performance estimators for computational chemistry methods the empirical Cumulative Distribution Function of absolute errors
    Journal of Chemical Physics, 2018
    Co-Authors: Pascal Pernot, Andreas Savin
    Abstract:

    Benchmarking studies in computational chemistry use reference datasets to assess the accuracy of a method through error statistics. The commonly used error statistics, such as the mean signed and mean unsigned errors, do not inform end-users on the expected amplitude of prediction errors attached to these methods. We show that, the Distributions of model errors being neither normal nor zero-centered, these error statistics cannot be used to infer prediction error probabilities. To overcome this limitation, we advocate for the use of more informative statistics, based on the empirical Cumulative Distribution Function of unsigned errors, namely, (1) the probability for a new calculation to have an absolute error below a chosen threshold and (2) the maximal amplitude of errors one can expect with a chosen high confidence level. Those statistics are also shown to be well suited for benchmarking and ranking studies. Moreover, the standard error on all benchmarking statistics depends on the size of the reference dataset. Systematic publication of these standard errors would be very helpful to assess the statistical reliability of benchmarking conclusions.

  • probabilistic performance estimators for computational chemistry methods the empirical Cumulative Distribution Function of absolute errors
    Journal of Chemical Physics, 2018
    Co-Authors: Pascal Pernot, Andreas Savin
    Abstract:

    Benchmarking studies in computational chemistry use reference datasets to assess the accuracy of a method through error statistics. The commonly used error statistics, such as the mean signed and mean unsigned errors, do not inform end-users on the expected amplitude of prediction errors attached to these methods. We show that, the Distributions of model errors being neither normal nor zero-centered, these error statistics cannot be used to infer prediction error probabilities. To overcome this limitation, we advocate for the use of more informative statistics, based on the empirical Cumulative Distribution Function of unsigned errors, namely, (1) the probability for a new calculation to have an absolute error below a chosen threshold and (2) the maximal amplitude of errors one can expect with a chosen high confidence level. Those statistics are also shown to be well suited for benchmarking and ranking studies. Moreover, the standard error on all benchmarking statistics depends on the size of the reference dataset. Systematic publication of these standard errors would be very helpful to assess the statistical reliability of benchmarking conclusions.Benchmarking studies in computational chemistry use reference datasets to assess the accuracy of a method through error statistics. The commonly used error statistics, such as the mean signed and mean unsigned errors, do not inform end-users on the expected amplitude of prediction errors attached to these methods. We show that, the Distributions of model errors being neither normal nor zero-centered, these error statistics cannot be used to infer prediction error probabilities. To overcome this limitation, we advocate for the use of more informative statistics, based on the empirical Cumulative Distribution Function of unsigned errors, namely, (1) the probability for a new calculation to have an absolute error below a chosen threshold and (2) the maximal amplitude of errors one can expect with a chosen high confidence level. Those statistics are also shown to be well suited for benchmarking and ranking studies. Moreover, the standard error on all benchmarking statistics depends on the size of the referenc...

Michael J Seiler - One of the best experts on this subject based on the ideXlab platform.

Pascal Pernot - One of the best experts on this subject based on the ideXlab platform.

  • probabilistic performance estimators for computational chemistry methods the empirical Cumulative Distribution Function of absolute errors
    Journal of Chemical Physics, 2018
    Co-Authors: Pascal Pernot, Andreas Savin
    Abstract:

    Benchmarking studies in computational chemistry use reference datasets to assess the accuracy of a method through error statistics. The commonly used error statistics, such as the mean signed and mean unsigned errors, do not inform end-users on the expected amplitude of prediction errors attached to these methods. We show that, the Distributions of model errors being neither normal nor zero-centered, these error statistics cannot be used to infer prediction error probabilities. To overcome this limitation, we advocate for the use of more informative statistics, based on the empirical Cumulative Distribution Function of unsigned errors, namely, (1) the probability for a new calculation to have an absolute error below a chosen threshold and (2) the maximal amplitude of errors one can expect with a chosen high confidence level. Those statistics are also shown to be well suited for benchmarking and ranking studies. Moreover, the standard error on all benchmarking statistics depends on the size of the reference dataset. Systematic publication of these standard errors would be very helpful to assess the statistical reliability of benchmarking conclusions.

  • probabilistic performance estimators for computational chemistry methods the empirical Cumulative Distribution Function of absolute errors
    Journal of Chemical Physics, 2018
    Co-Authors: Pascal Pernot, Andreas Savin
    Abstract:

    Benchmarking studies in computational chemistry use reference datasets to assess the accuracy of a method through error statistics. The commonly used error statistics, such as the mean signed and mean unsigned errors, do not inform end-users on the expected amplitude of prediction errors attached to these methods. We show that, the Distributions of model errors being neither normal nor zero-centered, these error statistics cannot be used to infer prediction error probabilities. To overcome this limitation, we advocate for the use of more informative statistics, based on the empirical Cumulative Distribution Function of unsigned errors, namely, (1) the probability for a new calculation to have an absolute error below a chosen threshold and (2) the maximal amplitude of errors one can expect with a chosen high confidence level. Those statistics are also shown to be well suited for benchmarking and ranking studies. Moreover, the standard error on all benchmarking statistics depends on the size of the reference dataset. Systematic publication of these standard errors would be very helpful to assess the statistical reliability of benchmarking conclusions.Benchmarking studies in computational chemistry use reference datasets to assess the accuracy of a method through error statistics. The commonly used error statistics, such as the mean signed and mean unsigned errors, do not inform end-users on the expected amplitude of prediction errors attached to these methods. We show that, the Distributions of model errors being neither normal nor zero-centered, these error statistics cannot be used to infer prediction error probabilities. To overcome this limitation, we advocate for the use of more informative statistics, based on the empirical Cumulative Distribution Function of unsigned errors, namely, (1) the probability for a new calculation to have an absolute error below a chosen threshold and (2) the maximal amplitude of errors one can expect with a chosen high confidence level. Those statistics are also shown to be well suited for benchmarking and ranking studies. Moreover, the standard error on all benchmarking statistics depends on the size of the referenc...

Jose F Paris - One of the best experts on this subject based on the ideXlab platform.

Yunlung Teng - One of the best experts on this subject based on the ideXlab platform.

  • adaptive sampling based on the Cumulative Distribution Function of order statistics to delineate heavy metal contaminated soils using kriging
    Environmental Pollution, 2005
    Co-Authors: Kaiwei Juang, Daryuan Lee, Yunlung Teng
    Abstract:

    Abstract Correctly classifying “contaminated” areas in soils, based on the threshold for a contaminated site, is important for determining effective clean-up actions. Pollutant mapping by means of kriging is increasingly being used for the delineation of contaminated soils. However, those areas where the kriged pollutant concentrations are close to the threshold have a high possibility for being misclassified. In order to reduce the misclassification due to the over- or under-estimation from kriging, an adaptive sampling using the Cumulative Distribution Function of order statistics (CDFOS) was developed to draw additional samples for delineating contaminated soils, while kriging. A heavy-metal contaminated site in Hsinchu, Taiwan was used to illustrate this approach. The results showed that compared with random sampling, adaptive sampling using CDFOS reduced the kriging estimation errors and misclassification rates, and thus would appear to be a better choice than random sampling, as additional sampling is required for delineating the “contaminated” areas.