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Probabilistic performance estimators for computational chemistry methods: Systematic improvement probability and

Pascal Pernot¹, Andreas Savin²

¹Institut de Chimie Physique, UMR8000, CNRS, Université Paris-Saclay, 91405 Orsay, France.

The Journal of Chemical Physics

|May 3, 2020

Abstract:

In Paper I [P. Pernot and A. Savin, J. Chem. Phys. 152, 164108 (2020)], we introduced the systematic improvement probability as a tool to assess the level of improvement on absolute errors to be expected when switching between two computational chemistry methods. We also developed two indicators based on robust statistics to address the uncertainty of ranking in computational chemistry benchmarks: P_inv, the inversion probability between two values of a statistic, and P_r, the ranking probability matrix. In this second part, these indicators are applied to nine data sets extracted from the recent benchmarking literature. We also illustrate how the correlation between the error sets might contain useful information on the benchmark dataset quality, notably when experimental data are used as reference.

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