metrics to add

[raybellwaves]

Keep this comment in this issue updated with metrics to add to xskillscore. Consolidate from other issues as well as comments that appear below. The format for inputting will be:

• METRIC_API_NAME (LONG_METRIC_NAME) [RELATED ISSUE (IF EXISTS)] {METRIC SOURCE/EQUATION}

The full list of metrics current in xskillscore can be found here. Remove issues from here once they are added.

Correlation Metrics

• pearson_r_auto (Pearson R Autocorrelation) [#205] {https://github.com/bradyrx/esmtools/blob/master/esmtools/stats.py#L171 }

Distance Metrics

• medape (Median Absolute Percentage Error)
• rmspe (Root Mean Square Percentage Error) [#46] {https://www.kaggle.com/c/rossmann-store-sales/overview/evaluation }
• msle (Mean Squared Log Error) [#47] {https://scikit-learn.org/stable/modules/generated/sklearn.metrics.mean_squared_log_error.html }
• crmse (Centered Root Mean Square Error) {https://solarforecastarbiter.org/metrics/#crmse}
• maape (Mean Arctangent Absolute Percentage Error) [#85] {https://github.com/xarray-contrib/xskillscore/issues/85#issuecomment-653135691 }
• explained_var (Explained Variance Score) [#213] {https://scikit-learn.org/stable/modules/model_evaluation.html#explained-variance-score }
• mean_pinball (Mean Pinball Loss) [#274] {https://scikit-learn.org/dev/modules/generated/sklearn.metrics.mean_pinball_loss.html}

Probabilistic Metrics

• brier_skill_score (Brier Skill Score) [#49] {https://github.com/xarray-contrib/xskillscore/issues/49#issue-526878892 }
• Add fair arg to crps_ensemble [#260] {? }
• crpss (Continuous Ranked Probability Skill Score) [#49] {https://github.com/pangeo-data/climpred/blob/main/climpred/metrics.py#L2176}
• rpss (Ranked Probability Skill Score) [#49] {https://github.com/pangeo-data/climpred/blob/main/climpred/tests/test_probabilistic.py#L252}
• brier score decomposition https://github.com/csiro-dcfp/doppyo/blob/6c423b32ce013933072fb1c176e502a16de15fa2/doppyo/skill.py#L868

Dichotomous-Only (yes/no) Metrics

• f1 (f1 Score) [#138] {https://scikit-learn.org/stable/modules/generated/sklearn.metrics.f1_score.html#sklearn.metrics.f1_score }
• tpr (True Positive Rate/Recall Score) [#138] {https://scikit-learn.org/stable/modules/generated/sklearn.metrics.recall_score.html#sklearn.metrics.recall_score }
• precision (Positive Predictive Value/Precision Score) {https://scikit-learn.org/stable/modules/generated/sklearn.metrics.precision_score.html#sklearn.metrics.precision_score }
• rel_value (Relative Value Score) [#229] {https://www.ecmwf.int/sites/default/files/elibrary/2007/15489-verification-probability-forecasts.pdf }

Multi-Category Metrics

• mc_threat_score (Multi-Category Threat Score) [#187] {?}

Comparative

• ttest_ind (T-test for the means of two independent samples of scores) [#175] {https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.ttest_ind.html }

Resampling

Metric glossaries:

• https://solarforecastarbiter.org/metrics/

[aaronspring]

what about brier_score with decomposition? nice explanation in https://timvangelder.com/2015/05/18/brier-score-composition-a-mini-tutorial/ implemented in https://github.com/csiro-dcfp/doppyo/blob/8c620889bde8a21d5937eb7ac71e72a040b31867/doppyo/skill.py#L868 with loop. do you think there is a solution without a loop @dougiesquire ?

[dougiesquire]

Sorry I've been on leave. I don't remember much about the brier_score implementation in doppyo, but I'm sure it could be improved. At the very least, we could implement the loop with numpy arrays and then wrap with apply_ufunc as is done for many of the other functions in xskillscore

[aaronspring]

• cost loss C/L metric

[raybellwaves]

https://github.com/google-research/weatherbench2/blob/main/weatherbench2/metrics.py