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REVIEW 3 major objections 4 minor 1 cited by

A Probabilistic WxChallenge Proposal

T0 review · 3 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read WxChallenge could score forecasts in bits by measuring information gained over an ensemble baseline, the paper proposes.

desk verdict Clear, honest proposal for probabilistic WxChallenge games, but the ranked information gain score is improper, so the central claim of soundness fails. read the letter →

arxiv 2501.14139 v1 pith:IPVAR6RF submitted 2025-01-23 stat.AP

John R. Lawson This is my paper · ORCID
classification stat.AP
keywords WxChallengeprobabilisticforecastinginformationgainproperscoringrulesspreadbettingbinnedprobabilityforecastsensemblebaselinesforecastverification
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The WxChallenge is a national weather-forecasting competition that currently scores deterministic forecasts with point rules that can be hedged and do not combine across variables. The paper proposes two optional probabilistic games: a spread bet on whether an observation exceeds an ensemble-derived threshold, and a ten-bin distribution game for continuous variables such as precipitation. Both games are scored by Shannon information gain over a baseline set by a morning ensemble, so skill is measured in additive bits. The paper argues that information gain is a sound, proper scoring rule that punishes hedging, and that its ranked form works as a multi-bin extension of the Brier and Ranked Probability Scores.

What carries the argument

The active ingredient is Shannon information gain, $IG_t = \log_2(f_t/b_t)$, which measures how much surprise the player's forecast removes relative to the baseline. A proper scoring rule is one whose expected value is maximized by reporting true beliefs, and the paper asserts that information gain has this property in the binary over/under case. The ranked version, $RIG = \sum_k g_k \log_2(f_k/b_k)$, is presented as an information-theoretic cousin of the Ranked Probability Score, with $g_k = +1$ for the observed bin and $-1$ otherwise. The baseline $b_t$ is generated automatically from 1200 UTC runs of ensemble guidance, providing a fixed threshold the player must beat, and the additivity of bits is what permits scores from different variables to be summed.

What would settle it

For a ten-bin categorical forecast with true probability vector $p$, compute the expected value of Eq. 5 for every forecast vector $f$, using $b_k = 0.1$ and $g_k = +1$ for the observed bin only; if the maximizer differs from $p$ for some $p$, the score is not proper and Game 2 is hedgeable.

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Extended reading notes

Core claim

The central claim is that WxChallenge skill can be measured as the information a player's forecast adds over an automated ensemble baseline, rather than as distance from the observed scalar. Writing the baseline probability as $b_t$ and the player's probability as $f_t$, the score is information gain $IG_t = \log_2(f_t/b_t)$, with units of bits because of the base-2 logarithm. For a binned continuous forecast, the paper adapts ranked ignorance into a ranked information gain $RIG = \sum_k g_k \log_2(f_k/b_k)$, where $g_k = +1$ for the verifying bin and $-1$ for all other bins. The paper claims that, like the Brier score, this approach is a proper scoring rule that discourages hedging, and that the additivity of bits means temperature, wind, and precipitation forecasts can be combined into a single skill score.

Load-bearing premise

The ranked information-gain score in Eq. 5 is assumed, without proof, to be a proper scoring rule; if maximizing its expected value does not make players report their true probabilities, the game can be hedged and the claim of scientific soundness fails.

Editorial extensions

If this is right

  • A player maximizing expected score in the over/under game should report their true probability of exceeding the threshold, rather than hedging toward a safe value.
  • Because all scores are in bits, skill at temperature, wind, and precipitation forecasting can be combined into one leaderboard number without rescaling.
  • New forecast variables, such as ice accumulation or dew point, could be added to the competition without redesigning the scoring system.
  • The automated ensemble baseline gives each forecast a clear bar: positive information gain means the player beat the raw model guidance.
  • Long-run player scores could be decomposed into reliability and discrimination, letting competitors see whether they are underconfident, overconfident, or poorly discriminating.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A natural next step before deployment is to check whether the ranked information gain in Eq. 5 remains a proper scoring rule for multi-bin forecasts, since properness of the binary case does not automatically carry over.
  • The paper's bin-width normalization through $b_k$ could be tested with unequal bins in probability space; changing bin widths may alter the score's information-theoretic interpretation.
  • Because baselines come from specific ensemble models, a player's bit score could depend on the quality and spread of those models; sensitivity tests across ensemble choices would clarify how much of the score reflects player skill.
  • The 100-credit allocation rule could be tested with fewer or more than ten bins to find the tradeoff between player burden and faithful approximation of the probability distribution.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The manuscript proposes two optional probabilistic forecast games for the WxChallenge competition. Game 1 asks players to allocate 100 confidence credits between over/under outcomes defined by 50th and 90th percentile thresholds from a 1200 UTC superensemble baseline; Game 2 asks players to distribute 100 credits across ten probability bins of a continuous variable such as precipitation. The paper proposes to score both games by Shannon information gain relative to the baseline (Eq. 3), and for Game 2 introduces a 'ranked information gain' (Eq. 5) with +1 weight on the observed bin and -1 on all other bins. The stated advantages are additivity in bits across variables and propriety, i.e., that the score punishes hedging and rewards honest probabilities.

Significance. The idea of adding accessible, optional probabilistic games to WxChallenge is attractive, and the binary over/under game with a log score against an ensemble baseline is a sensible design; the paper also correctly emphasizes the additivity of bits across variables. However, the manuscript's central quantitative claim is not supported: Eq. (5) is not a proper scoring rule, Table 1 contains sign errors, and the tunable floor in Section 6 introduces a post hoc fitting handle. As a proposal paper the contribution is primarily conceptual and could be of value to the forecasting-competition community if the scoring scheme is replaced with a genuinely proper ranked score; as submitted, the scientific-soundness claim fails.

major comments (3)
  1. [§6, Eq. (5)] The ranked information gain defined by Eq. (5) is not a proper scoring rule. If bin j verifies, RIG = 2 log2(f_j/b_j) - Σ_k log2(f_k/b_k); taking the expectation over the true distribution p gives E_p[RIG] = Σ_k (2p_k - 1) log2(f_k/b_k). The coefficient (2p_k - 1) is positive only for bins with p_k > 0.5, so the expected score is maximized by putting as much mass as allowed on high-probability bins and the minimum allowed mass on low-probability bins, not by reporting f = p. For example, with K = 10, b_k = 0.1, and p = (0.55, 0.05, ..., 0.05), the honest forecast f = p has expected score about 8.35 bits, while the extreme forecast f = (0.991, 0.001, ..., 0.001) has expected score about 54 bits. The floor p = 1/(4N) in Section 6 caps but does not remove this incentive. This directly contradicts the abstract and Section 3c, which state that information gain 'punishes hedging' and is a sound measure of skill. The citation to Tödter and Ahrens (2012), Eq. 27, does not support Eq. (5): their ranked ignorance is a sum over cumulative probabilities, not a weighted sum with g_k = ±1. Game 2 therefore does not reward honest probability reports as claimed.
  2. [Table 1] Table 1 contains sign errors. In the row f_t < b_t, the Observed column is printed as -log2(f_t/b_t). Since log2(f_t/b_t) is negative when f_t < b_t, this entry is positive, whereas the information gain for an observed event with f_t < b_t is log2(f_t/b_t), which is negative. In the Not Observed columns, the correct quantity is log2((1 - f_t)/(1 - b_t)), not ±log2(f_t/b_t). For instance, with b_t = 0.5 and f_t = 0.2, a non-event yields log2(0.8/0.5) = 0.678 bits, while the table's entry is log2(0.4) = -1.322 bits. These errors matter because Table 1 is the paper's explanation of how the score rewards or punishes forecasts relative to the baseline.
  3. [§6, p = 1/(4N)] The statement that the factor of four in the minimum probability floor p = 1/(4N) 'can be tuned to maximize skill after evaluation' makes the scoring rule depend on the competition's own outcomes. A positive score would then be the result of a post hoc fitted design choice rather than a fixed, pre-specified measure of skill. Because the floor directly controls how extreme the improper RIG forecasts can be, this tuning provision compounds the propriety problem in Eq. (5). A scientifically sound competition rule should fix the score and its bounds before forecasts are collected, and should validate the baseline against an independent reference rather than defining skill solely as deviation from the same superensemble used to set the thresholds.
minor comments (4)
  1. [§5] The coin-flip illustration has arithmetic slips: log2(0.8/0.5) = 0.678, not 0.67, and a missed heads gives log2(0.2/0.5) = -1.322, not -1.23; the subsequent expression '1 - 1.23 = 0.23' is therefore incorrect.
  2. [§6] The text says 'In Table 6 we represent each bin's forecast...' but the cited table is Table 1.
  3. [Abstract] The sentence 'highlighting need for more automation Hence I propose...' is missing a period or semicolon between 'automation' and 'Hence'.
  4. [§3] The name 'Kullback-Liebler Divergence' should be 'Kullback-Leibler Divergence'.

Circularity Check

1 steps flagged · score 6.0 of 10

Game 2's 'ranked information gain' is presented as a refactoring of the known proper RPS/RIGN family, but Eq. (5)'s own +1/-1 bin weighting makes the expected score maximized by extreme forecasts, not honest probabilities; the soundness claim rests on renaming rather than derivation.

  1. renaming known result [Section 6, Eq. (5), with Section 3 Eq. (4) and Section 7 summary]
    "Scores are evaluated with an analog of the Ranked Probability Score (RPS; Hersbach 2000): its information-theoretical cousin, Ranked Ignorance (RIGN; Tödter and Ahrens 2012)... RIG = Σ_k g_k log2(f_k/b_k)... I stress the above is not a coining of a 'new score' in a field awash with various evaluating scores, but simply a refactoring of RPS with information gain, i.e., deploying IG across a range of bins. Indeed, we can reformulate Eqn. 5 as in Eqn. 4, where RIGN from the forecast (ignorance over all bins) is subtracted from that of the baseline."

    The paper's claim that Game 2 is 'scientifically sound' rests on presenting Eq. (5) as 'simply a refactoring' of the known proper RPS/RIGN family and as equivalent to Eq. (4), the proper binary information gain. But by the paper's own definition (g_k = +1 for the observed bin and -1 for all others), the expected score under the true distribution p is Σ_k (2p_k-1) log2(f_k/b_k), whose maximizer is an extreme forecast, not f = p. For example, with 10 bins, b_k = 0.1, and p = (0.55, 0.05, ..., 0.05), the honest forecast scores about 8.35 bits while f = (0.99, 0.0011, ..., 0.0011) scores about 52.9 bits. Thus the propriety of RIGN/RPS is imported by renaming, not established for the actual equation; the 'punishment of hedging' conclusion is equivalent to the assertion that Eq.

full rationale

The binary information gain in Eq. (3) is a genuine proper score and gives Game 1 independent content, so the circularity is localized to Game 2. There, Eq. (5) is introduced as the 'information-theoretical cousin' of RIGN and as 'simply a refactoring' of RPS, and its ex-post maximizing property is read directly off its own g_k definition; no derivation of expected-score optimality is supplied, and the asserted identity with Eq. (4) is algebraically false. The ensemble-derived baseline and the tunable floor p = 1/(4N) are design choices rather than fitted predictions in this proposal, so they do not add circularity; the self-citation to Lawson et al. (2021) is not load-bearing. The fundamental defect in Eq. (5) is partly a correctness error, but the paper's own 'not a new score' framing makes the ranked game's advertised soundness rest on a renaming of a known proper score rather than on the actual defined functional.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The proposal relies on the ensemble baseline being calibrated, a proper scoring rule, and untested player engagement assumptions. The tunable floor parameter and chosen bin count are free choices that affect scores.

free parameters (3)
  • minimum probability floor p = 1/(4N) = 1/(4N), with the factor 4 stated as tunable
    Section 6: the author says the factor of four can be tuned to maximize skill after evaluation.
  • number of bins K = 10
    Section 6: chosen to balance approximation fidelity against player burden; affects score sensitivity.
  • percentile thresholds for Game 1 = 50th and 90th percentiles
    Section 4a: chosen for maximum entropy and excitement, not derived from data.
assumptions (4)
  • domain assumption The 1200 UTC superensemble percentiles are calibrated probabilities, so the fixed baseline b (0.5 or 0.1) is a fair reference.
    Section 4 assumes ensemble percentiles directly give thresholds and baseline probabilities without calibration against observations.
  • ad hoc to paper The ranked information gain in Eq. 5 is a proper scoring rule.
    Section 6 asserts the score is an analogue of RPS; no proof is given, and the assertion is false as written.
  • domain assumption Players will report true beliefs when allocating 100 confidence credits because the score is proper.
    The incentive-compatibility of the games rests on propriety of the score, which fails for Eq. 5.
  • domain assumption Players find the games accessible and enjoyable.
    Stated in the objective, but no empirical evidence is provided.

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Cite this review

Pith. "Pith review of A Probabilistic WxChallenge Proposal." pith.science (2026). https://pith.science/paper/IPVAR6RF

@misc{pith2026250114139,
  author       = {Pith},
  title        = {Pith review of: A Probabilistic WxChallenge Proposal},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IPVAR6RF}},
  note         = {Machine review of arXiv:2501.14139}
}
read the original abstract

The national forecasting competition WxChallenge, brainchild of Brad Illston at the University of Oklahoma in 2005, has become a cherished institution played across the United States each year. Participants include students, faculty, alumni, and industry professionals. However, forecasts are given as scalar values without expression of uncertainty, probabilities being a keystone of meteorological forecasting today, and previous attempts to add probabilistic elements to WxChallenge have failed partly due to challenges in making probability forecasting accessible to all, and inability to combine scores with different units while also appropriately rewarding forecasts using proper scoring rules. Much of the competition's maintenance relies on dedicated volunteers, highlighting need for more automation. Hence I propose three new features: (1) automated forecast problems based on morning ensemble guidance, forming prediction baselines, thresholds over which the players demonstrate skill in their later forecast; (2) a spread betting game, where the players allocate 100 confidence credits to the over-under for exceeding a percentile (e.g., 50pc) threshold of a variable (e.g., maximum temperature) derived from the ensemble baseline; and (3) a game where players distribute 100 confidence credits across bins of a continuous variable (e.g., accumulated precipitation) approximating a probability mass function. Forecasts are evaluated using Shannon information gained over the baseline forecast, yielding additive units of bits that allow score combinations of different variables and units. Information gain parallels the Brier Score and is likewise a sound measure of skill due its punishment of hedging. This proposal objective is to augment WxChallenge with two new probabilistic games that are accessible, scientifically sound, enjoyable, and optional.

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Intertwined Orders and the Physics of High Temperature Superconductors

    cond-mat.supr-con 2025-06 unverdicted novelty 1.0 of 10

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Reference graph

Works this paper leans on

52 extracted references · 45 canonical work pages · cited by 1 Pith paper

  1. [1]

    , " * write output.state after.block = add.period write newline

    ENTRY address archive author booktitle chapter doi edition editor eid eprint howpublished department institution journal key month note number organization pages publisher school series title type url volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 '...

  2. [2]

    write newline

    " write newline "" before.all 'output.state := FUNCTION if.digit duplicate "0" = swap duplicate "1" = swap duplicate "2" = swap duplicate "3" = swap duplicate "4" = swap duplicate "5" = swap duplicate "6" = swap duplicate "7" = swap duplicate "8" = swap "9" = or or or or or or or or or FUNCTION n.separate 't := "" #0 'numnames := t empty not t #-1 #1 subs...

  3. [3]

    Benedetti, R., 2010: Scoring rules for forecast verification. Mon. Weather Rev., 138 (1), 203--211

    work page 2010

  4. [4]

    Berner, J., and Coauthors, 2017: Stochastic parameterization: Toward a new view of weather and climate models. Bull. Amer. Meteor. Soc., 98 (3), 565--588

    work page 2017

  5. [5]

    Spiegelhalter, 2014: The Norm Chronicles: Stories and Numbers About Danger and Death

    Blastland, M., and D. Spiegelhalter, 2014: The Norm Chronicles: Stories and Numbers About Danger and Death. Basic Books

    work page 2014

  6. [6]

    W., 1950: Verification of forecasts expressed in terms of probability

    Brier, G. W., 1950: Verification of forecasts expressed in terms of probability. Mon. Weather Rev., 78 (1), 1--3

    work page 1950

  7. [7]

    2303.12712

    Bubeck, S., and Coauthors, 2023: Sparks of artificial general intelligence: Early experiments with GPT-4 . 2303.12712

    arXiv 2023

  8. [8]

    Buizza, R., 2001: Accuracy and potential economic value of categorical and probabilistic forecasts of discrete events. Mon. Weather Rev., 129 (9), 2329--2345

    work page 2001

Show all 52 references
  1. [9]

    M., and J

    Cover, T. M., and J. A. Thomas, 2012: Elements of Information Theory. John Wiley & Sons

    2012

  2. [10]

    Puntoni, and R

    de Langhe, B., S. Puntoni, and R. P. Larrick, 2017: Linear thinking in a nonlinear world. Harv. Bus. Rev., 2017 (May-June), 11

    2017

  3. [11]

    G., 2012: Development and analysis of a probabilistic forecasting game for meteorology students

    Decker, S. G., 2012: Development and analysis of a probabilistic forecasting game for meteorology students. Bull. Am. Meteorol. Soc., 93 (12), 1833--1843

    2012

  4. [12]

    part i: Measures of predictability

    DelSole, T., 2004: Predictability and information theory. part i: Measures of predictability. J. Atmos. Sci., 61 (20), 2425--2440

    2004

  5. [13]

    2304.03208

    Dey, N., and Coauthors, 2023: Cerebras-GPT : Open Compute-Optimal language models trained on the cerebras Wafer-Scale cluster. 2304.03208

    2023 arXiv

  6. [14]

    Saito, and H

    Duc, L., K. Saito, and H. Seko, 2013: Spatial-temporal fractions verification for high-resolution ensemble forecasts. Tellus Ser. A Dyn. Meteorol. Oceanogr., 65 (1), 18\,171

    2013

  7. [15]

    R., and J

    Durran, D. R., and J. A. Weyn, 2016: Thunderstorms do not get butterflies. Bull. Amer. Meteor. Soc., 97 (2), 237--243

    2016

  8. [16]

    Lavers, T

    Gasc \'o n, E., D. Lavers, T. M. Hamill, D. S. Richardson, Z. Ben Bouall \`e gue, M. Leutbecher, and F. Pappenberger, 2019: Statistical post-processing of dual-resolution ensemble precipitation forecasts across europe. Quart. J. Roy. Meteor. Soc., 0 (ja)

    2019

  9. [17]

    Complexity: Metaphors, Models, and Reality, Addison-Wesley

    Gell-Mann, M., 1994: Complex adaptive systems. Complexity: Metaphors, Models, and Reality, Addison-Wesley

    1994

  10. [18]

    Hertwig, E

    Gigerenzer, G., R. Hertwig, E. van den Broek, B. Fasolo, and K. V. Katsikopoulos, 2005: ``a 30\ understand probabilistic weather forecasts? Risk Anal., 25 (3), 623--629

    2005

  11. [19]

    Green, D. M., J. A. Swets, and Others , 1966: Signal detection theory and psychophysics, Vol. 1. Wiley New York

    1966

  12. [20]

    Hagelin, S., J. Son, R. Swinbank, A. McCabe, N. Roberts, and W. Tennant, 2017: The met office convective-scale ensemble, MOGREPS-UK . Quart. J. Roy. Meteor. Soc., 143 (708), 2846--2861

    2017

  13. [21]

    2303.13988

    Hagendorff, T., 2023: Machine psychology: Investigating emergent capabilities and behavior in large language models using psychological methods. 2303.13988

    2023 arXiv

  14. [22]

    Pei, and H

    Han, J., J. Pei, and H. Tong, 2022: Data Mining: Concepts and Techniques. Morgan Kaufmann

    2022

  15. [23]

    Weather Forecast., 15 (5), 559--570

    Hersbach, H., 2000: Decomposition of the continuous ranked probability score for ensemble prediction systems. Weather Forecast., 15 (5), 559--570

    2000

  16. [24]

    T., and D

    Jolliffe, I. T., and D. B. Stephenson, 2003: Forecast Verification: A Practitioner's Guide in Atmospheric Science. John Wiley & Sons

    2003

  17. [25]

    Macmillan

    Kahneman, D., 2011: Thinking, Fast and Slow. Macmillan

    2011

  18. [26]

    Krzysztofowicz, R., 2001: The case for probabilistic forecasting in hydrology. J. Hydrol., 249 (1), 2--9

    2001

  19. [27]

    Lawson, J. R., C. K. Potvin, P. S. Skinner, and A. E. Reinhart, 2021: The vice and virtue of increased horizontal resolution in ensemble forecasts of tornadic thunderstorms in low-CAPE , high-shear environments. Mon. Weather Rev., 149 (4), 921--944

    2021

  20. [28]

    N., 1963: Deterministic nonperiodic flow

    Lorenz, E. N., 1963: Deterministic nonperiodic flow. J. Atmos. Sci., 20, 130--141

    1963

  21. [29]

    J., 2008: Understanding forecast verification statistics

    Mason, S. J., 2008: Understanding forecast verification statistics. Met. Apps, 15 (1), 31--40

    2008

  22. [30]

    G., 2019: In favor of logarithmic scoring

    McCutcheon, R. G., 2019: In favor of logarithmic scoring. Philos. Sci., 86 (2), 286--303

    2019

  23. [31]

    P., 2013: A strategy for verifying Near-Convection-Resolving model forecasts at observing sites

    Mittermaier, M. P., 2013: A strategy for verifying Near-Convection-Resolving model forecasts at observing sites. Weather Forecast., 29 (2), 185--204

    2013

  24. [32]

    OpenAI , 2023: GPT-4 . Tech. rep

    2023

  25. [33]

    Palmer, T. N., A. D \"o ring, and G. Seregin, 2014: The real butterfly effect. Nonlinearity, 27 (9), R123

    2014

  26. [34]

    Peirolo, R., 2011: Information gain as a score for probabilistic forecasts. Met. Apps, 18 (1), 9--17

    2011

  27. [35]

    R., 1980: An Introduction to Information Theory: Symbols, Signals and Noise

    Pierce, J. R., 1980: An Introduction to Information Theory: Symbols, Signals and Noise. Dover Publications

    1980

  28. [36]

    Porson, A. N., S. Hagelin, D. F. A. Boyd, N. M. Roberts, R. North, S. Webster, and L. O. Jeff Chun‐Fung, 2019: Extreme rainfall sensitivity in convective‐scale ensemble modelling over singapore. Quart. J. Roy. Meteor. Soc

    2019

  29. [37]

    Franco-Pedroso, A

    Ramos, D., J. Franco-Pedroso, A. Lozano-Diez, and J. Gonzalez-Rodriguez, 2018: Deconstructing Cross-Entropy for probabilistic binary classifiers. Entropy, 20 (3)

    2018

  30. [38]

    Roberts, B., I. L. Jirak, A. J. Clark, S. J. Weiss, and J. S. Kain, 2019: PostProcessing and visualization techniques for Convection-Allowing ensembles. Bull. Am. Meteorol. Soc., 100 (7), 1245--1258

    2019

  31. [39]

    M., and H

    Roberts, N. M., and H. W. Lean, 2008: Scale-Selective verification of rainfall accumulations from high-resolution forecasts of convective events. Mon. Weather Rev., 136 (1), 78--97

    2008

  32. [40]

    J., 2013: Using evolutionary programming to generate skillful extreme value probabilistic forecasts

    Roebber, P. J., 2013: Using evolutionary programming to generate skillful extreme value probabilistic forecasts. Mon. Weather Rev., 141 (9), 3170--3185

    2013

  33. [41]

    Rothfusz, L. P., R. Schneider, D. Novak, K. Klockow-McClain, A. E. Gerard, C. Karstens, G. J. Stumpf, and T. M. Smith, 2018: FACETs : A proposed Next-Generation paradigm for High-Impact weather forecasting. Bull. Am. Meteorol. Soc., 99 (10), 2025--2043

    2018

  34. [42]

    S., and L

    Roulston, M. S., and L. A. Smith, 2002: Evaluating probabilistic forecasts using information theory. Mon. Weather Rev., 130 (6), 1653--1660

    2002

  35. [43]

    Sobash, R. A., C. S. Schwartz, G. S. Romine, K. R. Fossell, and M. L. Weisman, 2016: Severe weather prediction using storm surrogates from an ensemble forecasting system. Weather Forecast., 31 (1), 255--271

    2016

  36. [44]

    1908.09203

    Solaiman, I., and Coauthors, 2019: Release strategies and the social impacts of language models. 1908.09203

    2019 arXiv

  37. [45]

    Ahrens, 2012: Generalization of the ignorance score: Continuous ranked version and its decomposition

    T \"o dter, J., and B. Ahrens, 2012: Generalization of the ignorance score: Continuous ranked version and its decomposition. Mon. Weather Rev., 140 (6), 2005--2017

    2012

  38. [46]

    Walser, J

    Verbunt, M., A. Walser, J. Gurtz, A. Montani, and C. Sch \"a r, 2007: Probabilistic flood forecasting with a Limited-Area ensemble prediction system: Selected case studies. J. Hydrometeorol., 8 (4), 897--909

    2007

  39. [47]

    2112.04359

    Weidinger, L., and Coauthors, 2021: Ethical and social risks of harm from language models. 2112.04359

    2021 arXiv

  40. [48]

    V., and N

    Weijs, S. V., and N. van de Giesen, 2011: Accounting for observational uncertainty in forecast verification: An Information-Theoretical view on forecasts, observations, and truth. Mon. Weather Rev., 139 (7), 2156--2162

    2011

  41. [49]

    Weijs, S. V., R. van Nooijen, and N. van de Giesen, 2010: Kullback--Leibler divergence as a forecast skill score with classic Reliability--Resolution--Uncertainty decomposition. Mon. Weather Rev., 138 (9), 3387--3399

    2010

  42. [50]

    P., 1997: Chaos theory tamed

    Williams, G. P., 1997: Chaos theory tamed. Joseph Henry Press

    1997

  43. [51]

    Williams, R. M., C. A. T. Ferro, and F. Kwasniok, 2014: A comparison of ensemble post-processing methods for extreme events. Q.J.R. Meteorol. Soc., 140 (680), 1112--1120

    2014

  44. [52]

    Zakaria, 2019: Explanations for cultural differences in thinking: Easterners' dialectical thinking and westerners' linear thinking

    Yama, H., and N. Zakaria, 2019: Explanations for cultural differences in thinking: Easterners' dialectical thinking and westerners' linear thinking. J. Cogn. Psychol., 31 (4), 487--506

    2019

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