ROmondi/STST · Datasets at Hugging Face

text stringlengths 1 298
David D. Jackson, Sum Mak, David A. Rhoades, Matthew C. Gerstenberger, Naoshi Hirata, Maria Liukis,
Philip J. Maechling, Anne Strader, Matteo Taroni, Stefan Wiemer, Jeremy D. Zechar, and Jiancang
Zhuang. The collaboratory for the study of earthquake predictability: Achievements and priorities. Seis
mological Research Letters, 89(4):1305–1313, June 2018. ISSN 1938-2057. https://doi.org/10.1785/
0220180053.
Benedikt Schulz and Sebastian Lerch. Machine learning methods for postprocessing ensemble forecasts of
wind gusts: A systematic comparison. Monthly Weather Review, 150(1):235–257, January 2022. ISSN
1520-0493. https://doi.org/10.1175/mwr-d-21-0150.1.
C. E. Shannon. A mathematical theory of communication. Bell System Technical Journal, 27(4):623–656,
October 1948. ISSN 0005-8580. https://doi.org/10.1002/j.1538-7305.1948.tb00917.x.
Alex Smola, Arthur Gretton, Le Song, and Bernhard Schölkopf. A hilbert space embedding for distributions.
In Marcus Hutter, Rocco A. Servedio, and Eiji Takimoto, editors, Algorithmic Learning Theory, pages 13
31, Berlin, Heidelberg, 2007. Springer Berlin Heidelberg. ISBN 978-3-540-75225-7.
Joël Stein and Fabien Stoop. Neighborhood-based ensemble evaluation using the crps. Monthly Weather
Review, 150(8):1901–1914, August 2022. ISSN 1520-0493. https://doi.org/10.1175/mwr-d-21-0224.1.
Ingo Steinwart and Andreas Christmann. Support Vector Machines. Information Science and Statistics.
Springer, New York, 2008. ISBN 978-0-387-77241-7.
Ingo Steinwart and Johanna F. Ziegel. Strictly proper kernel scores and characteristic kernels on compact
spaces. Applied and Computational Harmonic Analysis, 51:510–542, 2021. ISSN 1063-5203. https:
//doi.org/10.1016/j.acha.2019.11.005. URL https://www.sciencedirect.com/science/article/
pii/S1063520317301483.
Gábor Székely. E-statistics: The energy of statistical samples. techreport, Bowling Green State University,
2003.
Maxime Taillardat. Skewed and mixture of gaussian distributions for ensemble postprocessing. Atmosphere,
12(8):966, July 2021. ISSN 2073-4433. https://doi.org/10.3390/atmos12080966.
Maxime Taillardat and Olivier Mestre. From research to applications– examples of operational ensemble
post-processing in france using machine learning. Nonlinear Processes in Geophysics, 27(2):329–347, May
2020. ISSN 1607-7946. https://doi.org/10.5194/npg-27-329-2020.
34
Maxime Taillardat, Olivier Mestre, Michaël Zamo, and Philippe Naveau. Calibrated ensemble forecasts
using quantile regression forests and ensemble model output statistics. Monthly Weather Review, 144(6):
2375–2393, June 2016. ISSN 1520-0493. https://doi.org/10.1175/mwr-d-15-0260.1.
O. Talagrand, R. Vautard, and B Strauss. Evaluation of probabilistic prediction systems. In Workshop on
Predictability, 20-22 October 1997, pages 1–26, Shinfield Park, Reading, 1997. ECMWF.
Thordis L. Thorarinsdottir and Nina Schuhen. Verification: Assessment of Calibration and Accuracy, pages
155–186. Elsevier, 2018. https://doi.org/10.1016/b978-0-12-812372-0.00006-6.
Thordis L. Thorarinsdottir, Tilmann Gneiting, and Nadine Gissibl. Using proper divergence functions to
evaluate climate models. SIAM/ASA Journal on Uncertainty Quantification, 1(1):522–534, January 2013.
ISSN 2166-2525. https://doi.org/10.1137/130907550.
Alexander Tsyplakov. Evaluating density forecasts: A comment. SSRN Electronic Journal, 2011. ISSN
1556-5068. https://doi.org/10.2139/ssrn.1907799.
Alexander Tsyplakov. Evaluation of probabilistic forecasts: Proper scoring rules and moments. SSRN
Electronic Journal, 2013. ISSN 1556-5068. https://doi.org/10.2139/ssrn.2236605.
Alexander Tsyplakov. Evaluation of probabilistic forecasts: Conditional auto-calibration, 2020. URL https:
//www.sas.upenn.edu/~fdiebold/papers2/Tsyplakov_Auto_calibration_sent_eswc2020.pdf.
Stéphane Vannitsem, John Bjørnar Bremnes, Jonathan Demaeyer, Gavin R. Evans, Jonathan Flowerdew,
Stephan Hemri, Sebastian Lerch, Nigel Roberts, Susanne Theis, Aitor Atencia, Zied Ben Bouallègue,
Jonas Bhend, Markus Dabernig, Lesley De Cruz, Leila Hieta, Olivier Mestre, Lionel Moret, Iris Odak
Plenković, Maurice Schmeits, Maxime Taillardat, Joris Van den Bergh, Bert Van Schaeybroeck, Kirien
Whan, and Jussi Ylhaisi. Statistical postprocessing for weather forecasts: Review, challenges, and avenues
in a big data world. Bulletin of the American Meteorological Society, 102(3):E681–E699, March 2021.
ISSN 1520-0477. https://doi.org/10.1175/bams-d-19-0308.1.
Heini Wernli, Marcus Paulat, Martin Hagen, and Christoph Frei. Sal—a novel quality measure for the
verification of quantitative precipitation forecasts. Monthly Weather Review, 136(11):4470–4487, November
2008. ISSN 0027-0644. https://doi.org/10.1175/2008mwr2415.1.
Andreas Winkelbauer. Moments and absolute moments of the normal distribution. September 2014. https:
//doi.org/10.48550/ARXIV.1209.4340.
R. L. Winkler, Javier Muñoz, José L. Cervera, José M. Bernardo, Gail Blattenberger, Joseph B. Kadane,
Dennis V. Lindley, Allan H. Murphy, Robert M Oliver, and David Ríos-Insua. Scoring rules and the
evaluation of probabilities. Test, 5(1):1–60, June 1996. ISSN 1863-8260. https://doi.org/10.1007/
bf02562681.
Robert L. Winkler. Rewarding Expertise in Probability Assessment, pages 127–140. Springer Netherlands,
1977. ISBN 9789401012768. https://doi.org/10.1007/978-94-010-1276-8_10.
Michaël Zamo and Philippe Naveau. Estimation of the continuous ranked probability score with limited
information and applications to ensemble weather forecasts. Mathematical Geosciences, 50(2):209–234,
November 2017. ISSN 1874-8953. https://doi.org/10.1007/s11004-017-9709-7.
Florian Ziel and Kevin Berk. Multivariate forecasting evaluation: On sensitive and strictly proper scoring
rules. 2019.
35
A Expected univariate scoring rules
A.1 Squared Error
For any F,G ∈ P2(R), the expectation of the squared error (2) is :
EG[SE(F,Y )] = (µF −µG)2 +σG2,
where µF is the mean of the distribution F and µG and σG2 are the mean and the variance of the distribution
G.
Proof.
EG[SE(F,Y )] = EG[(µF −Y)2]
=µ2
F −2 µFEG[Y]+EG[Y2]
Using the fact that E[X2] = Var(X)+E[X]2,
EG[SE(F,Y )] = µ2
F −2 µFµG +σ2
G +µ2
G
=(µF −µG)2 +σ2
G
A.2 Quantile Score
For any F,G ∈ P1(R), the expectation of the quantile score of level α (4) is :
F−1(α)
EG[QSα(F,Y)] =
−∞
(F−1(α) −y)G(dy)−α
(F−1(α) −y)G(dy);
R
=EG[QSα(G,Y)]+ (G(F−1(α))−α)(F−1(α)−G−1(α))−
Proof. Inspired by the proof of the propriety of the quantile score in Friederichs and Hense (2008).
EG[QSα(F,Y)] =
=
=
(1y≤F−1(α) − α)(F−1(α) −y)G(dy)

David D. Jackson, Sum Mak, David A. Rhoades, Matthew C. Gerstenberger, Naoshi Hirata, Maria Liukis,

Philip J. Maechling, Anne Strader, Matteo Taroni, Stefan Wiemer, Jeremy D. Zechar, and Jiancang

Zhuang. The collaboratory for the study of earthquake predictability: Achievements and priorities. Seis

mological Research Letters, 89(4):1305–1313, June 2018. ISSN 1938-2057. https://doi.org/10.1785/

0220180053.

Benedikt Schulz and Sebastian Lerch. Machine learning methods for postprocessing ensemble forecasts of

wind gusts: A systematic comparison. Monthly Weather Review, 150(1):235–257, January 2022. ISSN

1520-0493. https://doi.org/10.1175/mwr-d-21-0150.1.

C. E. Shannon. A mathematical theory of communication. Bell System Technical Journal, 27(4):623–656,

October 1948. ISSN 0005-8580. https://doi.org/10.1002/j.1538-7305.1948.tb00917.x.

Alex Smola, Arthur Gretton, Le Song, and Bernhard Schölkopf. A hilbert space embedding for distributions.

In Marcus Hutter, Rocco A. Servedio, and Eiji Takimoto, editors, Algorithmic Learning Theory, pages 13

31, Berlin, Heidelberg, 2007. Springer Berlin Heidelberg. ISBN 978-3-540-75225-7.

Joël Stein and Fabien Stoop. Neighborhood-based ensemble evaluation using the crps. Monthly Weather

Review, 150(8):1901–1914, August 2022. ISSN 1520-0493. https://doi.org/10.1175/mwr-d-21-0224.1.

Ingo Steinwart and Andreas Christmann. Support Vector Machines. Information Science and Statistics.

Springer, New York, 2008. ISBN 978-0-387-77241-7.

Ingo Steinwart and Johanna F. Ziegel. Strictly proper kernel scores and characteristic kernels on compact

spaces. Applied and Computational Harmonic Analysis, 51:510–542, 2021. ISSN 1063-5203. https:

//doi.org/10.1016/j.acha.2019.11.005. URL https://www.sciencedirect.com/science/article/

pii/S1063520317301483.

Gábor Székely. E-statistics: The energy of statistical samples. techreport, Bowling Green State University,

2003.

Maxime Taillardat. Skewed and mixture of gaussian distributions for ensemble postprocessing. Atmosphere,

12(8):966, July 2021. ISSN 2073-4433. https://doi.org/10.3390/atmos12080966.

Maxime Taillardat and Olivier Mestre. From research to applications– examples of operational ensemble

post-processing in france using machine learning. Nonlinear Processes in Geophysics, 27(2):329–347, May

2020. ISSN 1607-7946. https://doi.org/10.5194/npg-27-329-2020.

34

Maxime Taillardat, Olivier Mestre, Michaël Zamo, and Philippe Naveau. Calibrated ensemble forecasts

using quantile regression forests and ensemble model output statistics. Monthly Weather Review, 144(6):

2375–2393, June 2016. ISSN 1520-0493. https://doi.org/10.1175/mwr-d-15-0260.1.

O. Talagrand, R. Vautard, and B Strauss. Evaluation of probabilistic prediction systems. In Workshop on

Predictability, 20-22 October 1997, pages 1–26, Shinfield Park, Reading, 1997. ECMWF.

Thordis L. Thorarinsdottir and Nina Schuhen. Verification: Assessment of Calibration and Accuracy, pages

155–186. Elsevier, 2018. https://doi.org/10.1016/b978-0-12-812372-0.00006-6.

Thordis L. Thorarinsdottir, Tilmann Gneiting, and Nadine Gissibl. Using proper divergence functions to

evaluate climate models. SIAM/ASA Journal on Uncertainty Quantification, 1(1):522–534, January 2013.

ISSN 2166-2525. https://doi.org/10.1137/130907550.

Alexander Tsyplakov. Evaluating density forecasts: A comment. SSRN Electronic Journal, 2011. ISSN

1556-5068. https://doi.org/10.2139/ssrn.1907799.

Alexander Tsyplakov. Evaluation of probabilistic forecasts: Proper scoring rules and moments. SSRN

Electronic Journal, 2013. ISSN 1556-5068. https://doi.org/10.2139/ssrn.2236605.

Alexander Tsyplakov. Evaluation of probabilistic forecasts: Conditional auto-calibration, 2020. URL https:

//www.sas.upenn.edu/~fdiebold/papers2/Tsyplakov_Auto_calibration_sent_eswc2020.pdf.

Stéphane Vannitsem, John Bjørnar Bremnes, Jonathan Demaeyer, Gavin R. Evans, Jonathan Flowerdew,

Stephan Hemri, Sebastian Lerch, Nigel Roberts, Susanne Theis, Aitor Atencia, Zied Ben Bouallègue,

Jonas Bhend, Markus Dabernig, Lesley De Cruz, Leila Hieta, Olivier Mestre, Lionel Moret, Iris Odak

Plenković, Maurice Schmeits, Maxime Taillardat, Joris Van den Bergh, Bert Van Schaeybroeck, Kirien

Whan, and Jussi Ylhaisi. Statistical postprocessing for weather forecasts: Review, challenges, and avenues

in a big data world. Bulletin of the American Meteorological Society, 102(3):E681–E699, March 2021.

ISSN 1520-0477. https://doi.org/10.1175/bams-d-19-0308.1.

Heini Wernli, Marcus Paulat, Martin Hagen, and Christoph Frei. Sal—a novel quality measure for the

verification of quantitative precipitation forecasts. Monthly Weather Review, 136(11):4470–4487, November

2008. ISSN 0027-0644. https://doi.org/10.1175/2008mwr2415.1.

Andreas Winkelbauer. Moments and absolute moments of the normal distribution. September 2014. https:

//doi.org/10.48550/ARXIV.1209.4340.

R. L. Winkler, Javier Muñoz, José L. Cervera, José M. Bernardo, Gail Blattenberger, Joseph B. Kadane,

Dennis V. Lindley, Allan H. Murphy, Robert M Oliver, and David Ríos-Insua. Scoring rules and the

evaluation of probabilities. Test, 5(1):1–60, June 1996. ISSN 1863-8260. https://doi.org/10.1007/

bf02562681.

Robert L. Winkler. Rewarding Expertise in Probability Assessment, pages 127–140. Springer Netherlands,

1977. ISBN 9789401012768. https://doi.org/10.1007/978-94-010-1276-8_10.

Michaël Zamo and Philippe Naveau. Estimation of the continuous ranked probability score with limited

information and applications to ensemble weather forecasts. Mathematical Geosciences, 50(2):209–234,

November 2017. ISSN 1874-8953. https://doi.org/10.1007/s11004-017-9709-7.

Florian Ziel and Kevin Berk. Multivariate forecasting evaluation: On sensitive and strictly proper scoring

rules. 2019.

35

A Expected univariate scoring rules

A.1 Squared Error

For any F,G ∈ P2(R), the expectation of the squared error (2) is :

EG[SE(F,Y )] = (µF −µG)2 +σG2,

where µF is the mean of the distribution F and µG and σG2 are the mean and the variance of the distribution

G.

Proof.

EG[SE(F,Y )] = EG[(µF −Y)2]

=µ2

F −2 µFEG[Y]+EG[Y2]

Using the fact that E[X2] = Var(X)+E[X]2,

EG[SE(F,Y )] = µ2

F −2 µFµG +σ2

G +µ2

G

=(µF −µG)2 +σ2

G

A.2 Quantile Score

For any F,G ∈ P1(R), the expectation of the quantile score of level α (4) is :

F−1(α)

EG[QSα(F,Y)] =

−∞

(F−1(α) −y)G(dy)−α

(F−1(α) −y)G(dy);

R

=EG[QSα(G,Y)]+ (G(F−1(α))−α)(F−1(α)−G−1(α))−

Proof. Inspired by the proof of the propriety of the quantile score in Friederichs and Hense (2008).

EG[QSα(F,Y)] =

=

(1y≤F−1(α) − α)(F−1(α) −y)G(dy)