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In the first part of this study (Paper I), we introduced the systematicimprovement probability (SIP) as a tool to assess the level of improvement onabsolute errors to be expected when switching between two computationalchemistry methods. We developed also two indicators based on robust statisticsto address the uncertainty of ranking in computational chemistry benchmarks:Pinv , the inversion probability between two values of a statistic, and Pr ,the ranking probability matrix. In this second part, these indicators areapplied to nine data sets extracted from the recent benchmarking literature. Weillustrate also how the correlation between the error sets might contain usefulinformation on the benchmark dataset quality, notably when experimental dataare used as reference.

journal of chemical physics online/the journal of chemical physics/journal of chemical physics

Probabilistic performance estimators for computational chemistry  methods: Systematic Improvement Probability and Ranking Probability Matrix.  II. Applications