The DOI matches its Crossref record; 13 of the 13 references it cites were found in a registry or an index; 4 of the 8 sources its claims cite were checked for support.
Root mean square error (RMSE) or mean absolute error (MAE)? – Arguments against avoiding RMSE in the literature
Open accessPublished version of a preprint
Abstract
Abstract. Both the root mean square error (RMSE) and the mean absolute error (MAE) are regularly employed in model evaluation studies. Willmott and Matsuura (2005) have suggested that the RMSE is not a good indicator of average model performance and might be a misleading indicator of average error, and thus the MAE would be a better metric for that purpose. While some concerns over using RMSE raised by Willmott and Matsuura (2005) and Willmott et al. (2009) are valid, the proposed avoidance of RMSE in favor of MAE is not the solution. Citing the aforementioned papers, many researchers chose MAE over RMSE to present their model evaluation statistics when presenting or adding the RMSE measures could be more beneficial. In this technical note, we demonstrate that the RMSE is not ambiguous in its meaning, contrary to what was claimed by Willmott et al. (2009). The RMSE is more appropriate to represent model performance than the MAE when the error distribution is expected to be Gaussian. In addition, we show that the RMSE satisfies the triangle inequality requirement for a distance metric, whereas Willmott et al. (2009) indicated that the sums-of-squares-based statistics do not satisfy this rule. In the end, we discussed some circumstances where using the RMSE will be more beneficial. However, we do not contend that the RMSE is superior over the MAE. Instead, a combination of metrics, including but certainly not limited to RMSEs and MAEs, are often required to assess model performance.
Overview
AI snapshot
Written from the paper’s full text.
TL;DR
This technical note argues against the recommendation by Willmott and Matsuura (2005) and Willmott et al. (2009) to abandon RMSE in favor of MAE, showing that RMSE is not ambiguous in meaning and is more appropriate when errors are expected to be Gaussian. The authors also demonstrate that RMSE satisfies the triangle inequality required of a distance metric, contrary to the earlier claims, while concluding that a combination of metrics is often needed.
Key findings
- RMSE is not ambiguous in its meaning, contrary to Willmott et al. (2009); it is more appropriate than MAE when the error distribution is expected to be Gaussian, whereas MAE suits uniformly distributed errors.
- Using randomly generated zero-mean, unit-variance Gaussian pseudo-errors, RMSEs converge to the true standard deviation (SE = 1) once n ≥ 100, with standard deviation within 5% of truth; MAEs converge to 0.8, approximating the expectation of √(2/π). Neither metric is robust at n = 4 or n = 10.
- RMSE satisfies the triangle inequality required for a distance metric: the example in Willmott et al. (2009) (d(a,c)=4, d(a,b)=2, d(b,c)=3) actually represents the MSE, not the RMSE, and the L2-norm proof in Eqs. (5)–(7) shows RMSE does satisfy it.
- RMSE has practical advantages: it avoids absolute values (useful for gradients/sensitivities and data assimilation cost functions) and is generally better at discriminating among model results by weighting unfavorable conditions more heavily.
Methods
- Technical note / commentary design: no new observational dataset; the argument is analytical, using norm theory (L1- and L2-norms linked to MAE and RMSE) and a proof of the triangle inequality for the L2-norm.
- A Monte Carlo-style demonstration: five sets of pseudo-errors of size n = 4, 10, 100, 1000, 10 000, and 1000 000 drawn from a zero-mean, unit-variance Gaussian distribution with different random seeds, comparing RMSEs and MAEs (Table 1).
- Reference to prior empirical example: Chai et al. (2009) reported RMSE-to-MAE ratios of 1.63 to 2.29 for model NO2 column predictions versus SCIAMACHY satellite observations.
Limitations
- Stated by the authors: the analysis assumes unbiased errors and does not consider uncertainties from observation errors or the method used to compare model and observations; all statistics are less useful with limited sample sizes (e.g., n = 4 or 10), where presenting the errors themselves may be more appropriate; for non-normal distributions, additional moments (mean, variance, skewness, flatness) are needed; outliers several orders larger than other samples may justifiably be removed when sample numbers are limited, and systematic errors may need removal before computing RMSEs.
- Evident from the text: the demonstration relies on synthetic Gaussian pseudo-errors rather than real model–observation comparisons, so the convergence results are conditional on the Gaussian assumption; the authors explicitly do not claim RMSE is superior to MAE, so the note offers guidance rather than a definitive metric selection rule.
Model-written summary. Check it against the paper before relying on it.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
14 Own interpretation · 6 No basis given · 4 Supported · 3 Sources not found · 3 Own result · 1 No full text of the sources · 1 Not checked yet
Every source the paper cites for this claim was checked and supports it.
In the paper
“Using hypothetical sets of four errors, Willmott and Matsuura (2005) demonstrated that while keeping the MAE as a constant of 2.0, the RMSE varies from 2.0 to 4.0.”
§ Root mean square error (RMSE) or mean absolute error (MAE)? -Arguments against avoiding RMSE in the literature > 1 Introduction
What the sources say
- Supportedcites Willmott and Matsuura (2005) source
Table 1 identifies five hypothetical sets of four errors, and Section 3 says their RMSE increases as the error magnitudes become more variable. The paper gives the bounds as MAE ≤ RMSE ≤ √n × MAE; with four errors and an MAE of 2.0, those bounds are 2.0 and 4.0. Page numbers are unavailable in our copy. (LLM, conf=0.90)
boostedcorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- Supported
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“In addition, we show that the RMSE satisfies the triangle inequality requirement for a distance metric, whereas Willmott et al. (2009) indicated that the sums-ofsquares-based statistics do not satisfy this rule.”
- Also stated in: § 3 Triangle inequality of a metric · boosted
“This proves that RMSE satisfies the triangle inequality required for a distance function metric.”
- Also stated in: § 4 Summary and discussion · boosted
“In addition, we demonstrate that the RMSE satisfies the triangle inequality required for a distance function metric.”
§ Root mean square error (RMSE) or mean absolute error (MAE)? -Arguments against avoiding RMSE in the literature > Abstract
boosted- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- Also stated in: § 3 Triangle inequality of a metric · boosted
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“When the sample size reaches 100 or above, using the calculated RMSEs one can re-construct the error distribution close to its “truth” or “exact solution”, with its standard deviation within 5 % to its truth (i.e., SE = 1).”
§ Root mean square error (RMSE) or mean absolute error (MAE)? -Arguments against avoiding RMSE in the literature > 2 Interpretation of RMSE and MAE
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- The authors state this as an assumption: The errors are unbiased and follow a normal distribution when presenting the RMSE.
- The authors state this as an assumption: The uncertainties brought in by observation errors or the method used to compare model and observations are not considered.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“For instance, Table 1 shows that neither the RMSEs nor the MAEs are robust when only 4 or 10 samples are used to calculate those values.”
§ Root mean square error (RMSE) or mean absolute error (MAE)? -Arguments against avoiding RMSE in the literature > 2 Interpretation of RMSE and MAE
plainn = 10- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- The authors state this as an assumption: The errors are unbiased and follow a normal distribution when presenting the RMSE.
- The authors state this as an assumption: The uncertainties brought in by observation errors or the method used to compare model and observations are not considered.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The RMSE is more appropriate to represent model performance than the MAE when the error distribution is expected to be Gaussian.”
- Also stated in: § 1 Introduction · plain
“When the error distribution is expected to be Gaussian and there are enough samples, the RMSE has an advantage over the MAE to illustrate the error distribution.”
- Also stated in: § 4 Summary and discussion · plain
“We present that the RMSE is not ambiguous in its meaning, and it is more appropriate to use than the MAE when model errors follow a normal distribution.”
§ Root mean square error (RMSE) or mean absolute error (MAE)? -Arguments against avoiding RMSE in the literature > Abstract
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- Rests on an assumption: Model errors are likely to have a normal distribution rather than a uniform distribution.
- Also stated in: § 1 Introduction · plain
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Giving higher weighting to the unfavorable conditions, the RMSE usually is better at revealing model performance differences.”
§ Root mean square error (RMSE) or mean absolute error (MAE)? -Arguments against avoiding RMSE in the literature > 4 Summary and discussion
hedgeddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
In the paper
“The L1-norm and L2-norm are closely related to the MAE and the RMSE, respectively, as shown in Eqs. ( 3) and ( 4): Horn and Johnson, 1990).”
§ Root mean square error (RMSE) or mean absolute error (MAE)? -Arguments against avoiding RMSE in the literature > 3 Triangle inequality of a metric
What the sources say
- Not matchedcites Horn and Johnson, 1990
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- Not matched
In the paper
“In this technical note, we demonstrate that the RMSE is not ambiguous in its meaning, contrary to what was claimed by Willmott et al. (2009).”
- Also stated in: § 4 Summary and discussion · plain
“We present that the RMSE is not ambiguous in its meaning, and it is more appropriate to use than the MAE when model errors follow a normal distribution.”
§ Root mean square error (RMSE) or mean absolute error (MAE)? -Arguments against avoiding RMSE in the literature > Abstract
What the sources say
- Not matchedcites Willmott et al. (2009)
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
boosted- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- Also stated in: § 4 Summary and discussion · plain
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“One distinct advantage of RMSEs over MAEs is that RM-SEs avoid the use of absolute value, which is highly undesirable in many mathematical calculations.”
§ Root mean square error (RMSE) or mean absolute error (MAE)? -Arguments against avoiding RMSE in the literature > 4 Summary and discussion
boosteddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Similarly, one can readily show that, for several sets of errors with the same RMSE, the MAE would vary from set to set.”
§ Root mean square error (RMSE) or mean absolute error (MAE)? -Arguments against avoiding RMSE in the literature > 1 Introduction
hedgedcorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- Probably not a substantial claim. 10
- It may state two separate claims as one. 2
- The quote only partly states this claim. 1
Every source the paper cites for this claim was checked and supports it.
In the paper
“They summarized that the RMSE tends to become increasingly larger than the MAE (but not necessarily in a monotonic fashion) as the distribution of error magnitudes becomes more variable.”
§ Root mean square error (RMSE) or mean absolute error (MAE)? -Arguments against avoiding RMSE in the literature > 1 Introduction
What the sources say
- Supportedcites Willmott and Matsuura (2005) source
The Concluding Remarks state the attributed point directly, including the qualification that the increase need not be monotonic. (LLM, conf=0.95)
hedgedcorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
- Supported
Every source the paper cites for this claim was checked and supports it.
In the paper
“They concluded that the RMSE varies with the variability of the the error magnitudes and the total-error or averageerror magnitude (MAE), and the sample size n.”
§ Root mean square error (RMSE) or mean absolute error (MAE)? -Arguments against avoiding RMSE in the literature > 1 Introduction
What the sources say
- Supportedcites Willmott and Matsuura (2005) source
The Concluding Remarks state that RMSE depends on error-magnitude variability, MAE, and the square root of sample size. The claim says it varies with sample size n, which accurately conveys that dependence without asserting that the relationship is linear. (LLM, conf=0.93)
boostedcorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. It may state two separate claims as one.
- Supported
Every source the paper cites for this claim was checked and supports it.
In the paper
“Willmott and Matsuura (2005) have simply proved that the RMSE is not equivalent to the MAE, and one cannot easily derive the MAE value from the RMSE (and vice versa).”
§ Root mean square error (RMSE) or mean absolute error (MAE)? -Arguments against avoiding RMSE in the literature > 1 Introduction
What the sources say
- Supportedcites Willmott and Matsuura (2005) source
Section 3 describes an inconsistent relationship between MAE and RMSE, including cases where RMSE changes with error-magnitude variance. Section 4 explains that RMSE depends on MAE, the distribution of error magnitudes, and the number of errors. This supports the claim that the measures are not equivalent and that one cannot generally derive either value from the other alone. (LLM, conf=0.90)
boosted- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- Supported
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Table 1 shows that the MAEs converge to 0.8, an approximation to the expectation of 2 π .”
§ Root mean square error (RMSE) or mean absolute error (MAE)? -Arguments against avoiding RMSE in the literature > 2 Interpretation of RMSE and MAE
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
The quote only partly states this claim.
- The authors state this as an assumption: The errors are unbiased and follow a normal distribution when presenting the RMSE.
- The authors state this as an assumption: The uncertainties brought in by observation errors or the method used to compare model and observations are not considered.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“When both metrics are calculated, the RMSE is by definition never smaller than the MAE.”
§ Root mean square error (RMSE) or mean absolute error (MAE)? -Arguments against avoiding RMSE in the literature > 1 Introduction
boosted- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The MAE is suitable to describe uniformly distributed errors.”
§ Root mean square error (RMSE) or mean absolute error (MAE)? -Arguments against avoiding RMSE in the literature > 2 Interpretation of RMSE and MAE
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“For other kinds of distributions, more statistical moments of model errors, such as mean, variance, skewness, and flatness, are needed to provide a complete picture of the model error variation.”
§ Root mean square error (RMSE) or mean absolute error (MAE)? -Arguments against avoiding RMSE in the literature > 4 Summary and discussion
plain- Asserted: passes — The authors put it forward as true.
- Checkable: fails — It may be too vague to check against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. It may be too vague to check against evidence. The paper’s conclusions may not depend on it.
In the paper
“The ratio of RMSE to MAE ranged from 1.63 to 2.29 (see Table 1 of Chai et al., 2009).”
§ Root mean square error (RMSE) or mean absolute error (MAE)? -Arguments against avoiding RMSE in the literature > 1 Introduction
What the sources say
- Not checked — no full text of the sourcecites Chai et al., 2009 source
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In many of the model sensitivity studies that use only RMSE, a detailed interpretation is not critical because variations of the same model will have similar error distributions.”
§ Root mean square error (RMSE) or mean absolute error (MAE)? -Arguments against avoiding RMSE in the literature > 4 Summary and discussion
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“As every statistical measure condenses a large number of data into a single value, it only provides one projection of the model errors emphasizing a certain aspect of the error characteristics of the model performance.”
- Also stated in: § 4 Summary and discussion · plain
“As stated earlier, any single metric provides only one projection of the model errors and, therefore, only emphasizes a certain aspect of the error characteristics.”
§ Root mean square error (RMSE) or mean absolute error (MAE)? -Arguments against avoiding RMSE in the literature > 1 Introduction
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: fails — It may be too vague to check against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. It may be too vague to check against evidence.
- Also stated in: § 4 Summary and discussion · plain
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“A combination of metrics, including but certainly not limited to RMSEs and MAEs, are often required to assess model performance.”
- Also stated in: § 4 Summary and discussion · plain
“A combination of metrics, including but certainly not limited to RMSEs and MAEs, are often required to assess model performance.”
§ Root mean square error (RMSE) or mean absolute error (MAE)? -Arguments against avoiding RMSE in the literature > Abstract
plain- Asserted: passes — The authors put it forward as true.
- Checkable: fails — It may be too vague to check against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. It may be too vague to check against evidence.
- Also stated in: § 4 Summary and discussion · plain
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“While the MAE gives the same weight to all errors, the RMSE penalizes variance as it gives errors with larger absolute values more weight than errors with smaller absolute values.”
§ Root mean square error (RMSE) or mean absolute error (MAE)? -Arguments against avoiding RMSE in the literature > 1 Introduction
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
The authors state this as an assumption.
The errors are unbiased and follow a normal distribution when presenting the RMSE.
“The underlying assumption when presenting the RMSE is that the errors are unbiased and follow a normal distribution.”
“We also assume the error sample set is unbiased.”
The paper relies on this without support.
Model errors are likely to have a normal distribution rather than a uniform distribution.
“Because model errors are likely to have a normal distribution rather than a uniform distribution, the RMSE is a better metric to present than the MAE for such a type of data.”
The authors state this as an assumption.
The uncertainties brought in by observation errors or the method used to compare model and observations are not considered.
“The uncertainties brought in by observation errors or the method used to compare model and observations are not considered here.”
The paper relies on this without support.
There are often hundreds of observations available to calculate model statistics.
“Fortunately, there are often hundreds of observations available to calculate model statistics, unlike the examples with n = 4 (Willmott and Matsuura, 2005) and n = 10 ( Willmott et al., 2009).”
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
§ Root mean square error (RMSE) or mean absolute error (MAE)? -Arguments against avoiding RMSE in the literature > 4 Summary and discussion
“| 4 | 0.92, 0.65, 1.48, 1.02, 0.79 0.70, 0.57, 1.33, 1.16, 0.76 | |”
§ Root mean square error (RMSE) or mean absolute error (MAE)? -Arguments against avoiding RMSE in the literature > 1 Introduction
“When both metrics are calculated, the RMSE is by definition never smaller than the MAE.”
Citations
Cites
Horn, R. A., & Johnson, C. R. (1985) · Cited by 22,203
David, F. N., & Tukey, J. W. (1977) · Biometrics · doi:10.2307/2529486 · Cited by 12,707
Willmott, C., & Matsuura, K. (2005) · Climate Research · doi:10.3354/cr030079 · Cited by 6,512 · cited 4×
“Further, Willmott et al. (2009) concluded that the sums-of-squaresbased error statistics such as the RMSE and the standard error have inherent ambiguities and recommended the use of alternates such as the MAE.”
BackgroundMethodInfluentialHuber, P. J., & Ronchetti, E. M. (2009) · Wiley series in probability and statistics · doi:10.1002/9780470434697 · Cited by 1,823
Ambiguities inherent in sums-of-squares-based error statistics
Willmott, C. J., Matsuura, K., & Robeson, S. M. (2008) · Atmospheric Environment · doi:10.1016/j.atmosenv.2008.10.005 · Cited by 212 · cited 1×
“Fortunately, there are often hundreds of observations available to calculate model statistics, unlike the examples with n= 4 (Willmott and Matsuura, 2005) and n= 10 (Willmott et al., 2009).”
BackgroundMcKeen, S. A., Wilczak, J. M., Grell, G., et al. (2005) · Journal of Geophysical Research Atmospheres · doi:10.1029/2005jd005858 · Cited by 208
Savage, N., Agnew, P., Davis, L. S., Ordóñez, C., Thorpe, R., Johnson, C. E., O’Connor, F. M., & Dalvi, M. (2013) · Geoscientific model development · doi:10.5194/gmd-6-353-2013 · Cited by 128
Taylor, M. H., Lösch, M., Wenzel, M., et al. (2013) · Journal of Climate · doi:10.1175/jcli-d-13-00089.1 · Cited by 93
Chai, T., Kim, H. C., Lee, P., et al. (2013) · Geoscientific model development · doi:10.5194/gmd-6-1831-2013 · Cited by 87
Self-citationA multi-physics ensemble of present-day climate regional simulations over the Iberian Peninsula
Jerez, S., Montávez, J. P., Jiménez‐Guerrero, P., et al. (2012) · Climate Dynamics · doi:10.1007/s00382-012-1539-1 · Cited by 80 · cited 2×
“(2009) (e.g., Taylor et al., 2013; Chatterjee et al., 2013; Jerez et al., 2013).”
Method
Cited by
Sorted by citations
Items 1,101–1,200 of 7,174
Performance and Cost Evaluation of Public Blockchain: An NFT Marketplace Case Study
Rasolroveicy, M., & Fokaefs, M. (2022) · Conference on Blockchain Research & Applications for Innovative Networks and Services (BRAINS) · doi:10.1109/brains55737.2022.9908999 · Cited by 27
Rajput, J., Singh, M., Lal, K., Khanna, M., Sarangi, A., Mukherjee, J., & Singh, S. K. (2023) · Water Science & Technology · doi:10.2166/wst.2023.137 · Cited by 27
Prediction of Cooling Load of Tropical Buildings with Machine Learning
Bekdaş, G., Aydın, Y., Işıkdağ, Ü., et al. (2023) · Sustainability · doi:10.3390/su15119061 · Cited by 27
Detection and counting of root-knot nematodes using YOLO models with mosaic augmentation
Pun, T. B., Neupane, A., Koech, R., et al. (2023) · Biosensors and Bioelectronics X · doi:10.1016/j.biosx.2023.100407 · Cited by 27
Ahmed, N., Aldaw, M., Ahmed, R. M., & Teodoriu, C. (2023) · Engineering Failure Analysis · doi:10.1016/j.engfailanal.2023.107864 · Cited by 27
Stabilization of Expansive Clays with Basalt Fibers and Prediction of Strength by Machine Learning
Sert, S., Arslan, E., Ocakbaşı, P., et al. (2024) · Arabian Journal for Science and Engineering · doi:10.1007/s13369-024-08752-w · Cited by 27
Mekyska, J., Galáž, Z., Kiska, T., Zvončák, V., Mucha, J., Smékal, Z., Eliasova, I., Košťálová, M., Mračková, M., Fiedorová, D., et al. (2018) · Cognitive Computation · doi:10.1007/s12559-018-9575-8 · Cited by 27
Spatial and Temporal Rainfall Variability over the Mountainous Central Pindus (Greece)
Stefanidis, S. P., & Stathis, D. (2018) · Climate · doi:10.3390/cli6030075 · Cited by 27
Chiao, W.-T., Syu, C.-H., Chen, B.-C., et al. (2018) · Ecotoxicology and Environmental Safety · doi:10.1016/j.ecoenv.2018.11.061 · Cited by 27
Torres-Martínez, J. A., Mora, A., Ramos‐Leal, J. A., et al. (2019) · Hydrogeology Journal · doi:10.1007/s10040-019-02024-w · Cited by 27
A critical analysis of metrics used for measuring progress in artificial intelligencePreprint
Blagec, K., Dorffner, G., Moradi, M., & Samwald, M. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2008.02577 · Cited by 60
Cabeza‐Gil, I., Ríos-Ruíz, I., Martínez, M. Á., et al. (2023) · Journal of Food Engineering · doi:10.1016/j.jfoodeng.2023.111697 · Cited by 26
Applying sustainable development goals in financial forecasting using machine learning techniques
Chang, A., Lee, T., & Lee, H. (2023) · Corporate Social Responsibility and Environmental Management · doi:10.1002/csr.2694 · Cited by 26
Review of machine learning methods for sea level change modeling and prediction
Ayinde, A. S., Huaming, Y. U., & Kejian, W. (2024) · The Science of The Total Environment · doi:10.1016/j.scitotenv.2024.176410 · Cited by 28
Ding, S., He, D., & Liu, G. (2024) · Electronics · doi:10.3390/electronics13245023 · Cited by 26
Machine Learning-Based Prediction of Tribological Properties of Epoxy Composite Coating
Yan, H., Junling, T., Chen, H., et al. (2025) · Polymers · doi:10.3390/polym17030282 · Cited by 26
Bjånes, D. A., Kellis, S., Nickl, R., Baker, B., Aflalo, T., Bashford, L., Chivukula, S., Fifer, M. S., Osborn, L. E., Christie, B., et al. (2025) · Acta Biomaterialia · doi:10.1016/j.actbio.2025.02.030 · Cited by 37
Impact of temperature and flow rate on oxygen dynamics and water quality in major Turkish rivers
Yavuz, V. S. (2025) · Scientific Reports · doi:10.1038/s41598-025-06433-8 · Cited by 26
Evaluation and spatial downscaling of CRU TS precipitation data in the Philippines
Salvacion, A. R., Magcale-Macandog, D. B., Cruz, P. C. S., Saludes, R. B., Pangga, I. B., & Cumagun, C. J. R. (2018) · Modeling Earth Systems and Environment · doi:10.1007/s40808-018-0477-2 · Cited by 27
Inertial Sensors are a Valid Tool to Detect and Consistently Quantify Jumping
Spangler, R., Rantalainen, T., Gastin, P. B., & Wundersitz, D. W. T. (2018) · International Journal of Sports Medicine · doi:10.1055/s-0044-100793 · Cited by 26
iBike: Intelligent public bicycle services assisted by data analytics
Zhang⋆, Y., Wen, H., Qiu, F., Wang, Z., & Abbas, H. (2018) · Future Generation Computer Systems · doi:10.1016/j.future.2018.12.017 · Cited by 26
Kodur, S., Shrestha, U. B., Maraseni, T., & Deo, R. C. (2019) · Journal of Cleaner Production · doi:10.1016/j.jclepro.2019.03.079 · Cited by 27
Zhang, C., Li, Q., Meng, L., & Ren, Y. (2019) · Journal of Biomolecular Structure and Dynamics · doi:10.1080/07391102.2019.1590244 · Cited by 27
Yin, Z., Feng, Q., Yang, L., et al. (2019) · International Journal of Climatology · doi:10.1002/joc.6435 · Cited by 26
A Sequential Ensemble Model for Communicable Disease Forecasting
Sultana, N., Sharma, N., Sharma, K. P., et al. (2019) · Current Bioinformatics · doi:10.2174/1574893614666191202153824 · Cited by 26
Chung, M. H. (2020) · Advances in Civil Engineering · doi:10.1155/2020/8701368 · Cited by 26
Prediksi Rerata Harga Beras Tingkat Grosir Indonesia dengan Long Short Term Memory
Sanjaya, F. I., & Heksaputra, D. (2020) · JATISI (Jurnal Teknik Informatika dan Sistem Informasi) · doi:10.35957/jatisi.v7i2.388 · Cited by 26
A Generative Approach Towards Improved Robotic Detection of Marine Litter
Hong, J., Fulton, M., & Sattar, J. (2020) · Proceedings - IEEE International Conference on Robotics and Automation/Proceedings · doi:10.1109/icra40945.2020.9197575 · Cited by 26
Hao, X., Xu, Q., Shi, X., et al. (2021) · Environmental Science and Pollution Research · doi:10.1007/s11356-021-12834-9 · Cited by 26
Green Inhibitor Performance against CaCO3 Scaling: Rate-Modeling Aided Test Procedure
Wedenig, M., Boch, R., Leis, A., Wagner, H., & Dietzel, M. (2021) · Crystal Growth & Design · doi:10.1021/acs.cgd.0c01258 · Cited by 26
Uncertainty of the 2D Resistivity Survey on the Subsurface Cavities
Doyoro, Y. G., Chang, P.-Y., & Puntu, J. M. (2021) · Applied Sciences · doi:10.3390/app11073143 · Cited by 26
Ye, L., Zahra, M. M. A., Al-Bedyry, N. K., et al. (2021) · Stochastic Environmental Research and Risk Assessment · doi:10.1007/s00477-021-02055-4 · Cited by 26
Lin, R. F.-Y., Ou, C., Tseng, K.-K., et al. (2021) · Technological Forecasting and Social Change · doi:10.1016/j.techfore.2021.121067 · Cited by 26
Qiao, L., Zhu, J., & Wang, Y. (2021) · steel research international · doi:10.1002/srin.202100267 · Cited by 26
Binarti, F., Koerniawan, M. D., Sugeng Triyadi, S., et al. (2021) · Sustainable Cities and Society · doi:10.1016/j.scs.2021.103457 · Cited by 26
Spatiotemporal Geostatistical Analysis and Global Mapping of CH4 Columns from GOSAT Observations
Li, L., Lei, L., Song, H., Zeng, Z., & He, Z. (2022) · Remote Sensing · doi:10.3390/rs14030654 · Cited by 29
Positional accuracy assessment of historical Google Earth imagery in Lagos State, Nigeria
Nwilo, P. C., Okolie, C. J., Onyegbula, J., et al. (2022) · Applied Geomatics · doi:10.1007/s12518-022-00449-9 · Cited by 26
Sar2color: Learning Imaging Characteristics of SAR Images for SAR-to-Optical Transformation
Guo, Z., Guo, H., Liu, X., Zhou, W., Wang, Y., & Fan, Y. (2022) · Remote Sensing · doi:10.3390/rs14153740 · Cited by 28
Qi, C., Huang, B., Wu, M., Wang, K., Yang, S. L., & Li, G. (2022) · Materials · doi:10.3390/ma15155369 · Cited by 26
Pappert, D., Barriendos, M., Brugnara, Y., et al. (2022) · Climate of the past · doi:10.5194/cp-18-2545-2022 · Cited by 26
Design of an Energy Pile Based on CPT Data Using Soft Computing Techniques
Kumar, P., & Samui, P. (2022) · Infrastructures · doi:10.3390/infrastructures7120169 · Cited by 27
Suryavanshi, P., Wang, J., Duggal, I., et al. (2023) · Pharmaceutics · doi:10.3390/pharmaceutics15041266 · Cited by 26
Sousa, A., Veloso, D. T., Gonçalves, H., Faria, J. P., Mendes‐Moreira, J., Graça, R., Gomes, D., Castro, R. S. E., & Henriques, P. C. (2023) · IEEE Access · doi:10.1109/access.2023.3307310 · Cited by 27
Nafari, R. H., Ngo, T., & Lehman, W. P. (2016) · International Journal of Disaster Risk Reduction · doi:10.1016/j.ijdrr.2016.03.007 · Cited by 26
Assessment of evaluation methods using infiltration data measured in heterogeneous mountain soils
Jačka, L., Pavlásek, J., Pech, P., et al. (2016) · Geoderma · doi:10.1016/j.geoderma.2016.04.023 · Cited by 26
Microarray Missing Value Imputation: A Regularized Local Learning Method
Wang, A., Chen, Y., An, N., et al. (2018) · IEEE Transactions on Computational Biology and Bioinformatics · doi:10.1109/tcbb.2018.2810205 · Cited by 26
Tahmasbian, I., Bai, S. H., Wang, Y., Boyd, S. E., Zhou, J. W., Esmaeilani, R., & Xu, Z. H. (2018) · CATENA · doi:10.1016/j.catena.2018.04.023 · Cited by 26
Krug, R. C., Cañeiro, J. P., Ribeiro, D. C., Darlow, B. J. S., Silva, M. F., & Loss, J. F. (2020) · Brazilian Journal of Physical Therapy · doi:10.1016/j.bjpt.2020.07.001 · Cited by 28
Estimation of sea state parameters from ship motion responses using attention-based neural networks
Selimović, D., Hržić, F., Prpić-Oršić, J., & Lerga, J. (2023) · Ocean Engineering · doi:10.1016/j.oceaneng.2023.114915 · Cited by 26
Bai, X., Cheng, W.-C., Wu, B., et al. (2023) · Acta Geotechnica · doi:10.1007/s11440-023-01902-8 · Cited by 25
Lawal, A. I., Hosseini, S., Kim, M., et al. (2023) · Natural Hazards · doi:10.1007/s11069-023-06275-5 · Cited by 25
Prediction of underground mining-induced subsidence: Artificial neural network based approach
Long, N. Q., Le, T. T. T., Trọng, N. G., et al. (2023) · Mining of Mineral Deposits · doi:10.33271/mining17.04.045 · Cited by 25
Lv, Y., Li, Z., Yuan, R. B., et al. (2024) · IEEE Transactions on Instrumentation and Measurement · doi:10.1109/tim.2024.3370808 · Cited by 25
Yu, X. B., Yin, D., Xu, H., Pinto, F., Schmidhalter, U., Nie, C., Bai, Y., Sankaran, S., Ming, B., Cui, N., et al. (2024) · Precision Agriculture · doi:10.1007/s11119-024-10135-y · Cited by 27
Complete-arch accuracy of seven intraoral scanners measured by the virtual-fit method
Borbola, D., Mikolicz, Á., Romanszky, L., Sersli, G., DeFee, M. R., Renné, W. G., & Vág, J. (2024) · Journal of Dentistry · doi:10.1016/j.jdent.2024.105281 · Cited by 27
Multifeature Fusion Method with Metaheuristic Optimization for Automated Voice Pathology Detection
Özbay, E., Ozbay, F. A., Khodadadi, N., Gharehchopogh, F. S., & Mirjalili, S. (2024) · Journal of Voice · doi:10.1016/j.jvoice.2024.08.018 · Cited by 25
Ghaffari, A., Shahbazi, Y., Kashavar, M. M., et al. (2024) · Buildings · doi:10.3390/buildings14103261 · Cited by 25
Yavuz, V. S. (2025) · Journal of Water and Climate Change · doi:10.2166/wcc.2025.798 · Cited by 25
Li, S., Wong, M. S., Zhu, R., Shi, G., & Yang, J. (2025) · Sustainable Cities and Society · doi:10.1016/j.scs.2025.106257 · Cited by 26
Li, H., Zhang, Y., Li, Y., Lam, J. S. L., Matthews, C., & Yang, Z. (2025) · Transportation Research Part E Logistics and Transportation Review · doi:10.1016/j.tre.2025.104072 · Cited by 26
Morrison, A., McGrath, D., & Wallace, E. S. (2017) · Journal of Sports Sciences · doi:10.1080/02640414.2017.1303187 · Cited by 25
Mehdipour, V., & Memarianfard, M. (2017) · Civil Engineering Journal · doi:10.28991/cej-030984 · Cited by 26
A Quantum Lightning Search Algorithm-Based Fuzzy Speed Controller for Induction Motor Drive
Hannan, M. A., Ali, J. A., Hussain, A., et al. (2017) · IEEE Access · doi:10.1109/access.2017.2778081 · Cited by 25
Ahmadvand, M., Soltani, J., Garmdareh, S. E. H., & Varavipour, M. (2018) · Environmental Health Engineering and Management · doi:10.15171/ehem.2018.10 · Cited by 27
Deo, R. C., Downs, N. J., Adamowski, J., et al. (2018) · Food and Energy Security · doi:10.1002/fes3.151 · Cited by 25
Improving Nighttime Light Imagery With Location-Based Social Media Data
Zhao, N., Zhang, W., Liu, Y., et al. (2018) · IEEE Transactions on Geoscience and Remote Sensing · doi:10.1109/tgrs.2018.2871788 · Cited by 25
Liu, G., Zhang, K., Chen, X., et al. (2018) · Journal of Lightwave Technology · doi:10.1109/jlt.2018.2883898 · Cited by 25
Keshtegar, B., Heddam, S., & Hosseinabadi, H. (2019) · Environmental Earth Sciences · doi:10.1007/s12665-018-8028-8 · Cited by 24
Predictive Model for Growth of Bacillus cereus at Temperatures Applicable to Cooling of Cooked Pasta
Juneja, V. K., Golden, C. E., Mishra, A., et al. (2019) · Journal of Food Science · doi:10.1111/1750-3841.14448 · Cited by 25
Karahalil, E., Germeç, M., Karaoğlan, M., et al. (2019) · Biomass Conversion and Biorefinery · doi:10.1007/s13399-019-00487-1 · Cited by 25
Shrestha, L., Crichton, S. O. J., Kulig, B., Kiesel, B., Hensel, O., & Sturm, B. (2019) · Thermal Science and Engineering Progress · doi:10.1016/j.tsep.2019.100461 · Cited by 23
Viellechner, A., & Spinler, S. (2020) · Proceedings of the ... Annual Hawaii International Conference on System Sciences/Proceedings of the Annual Hawaii International Conference on System Sciences · doi:10.24251/hicss.2020.158 · Cited by 25
Park, J. H., Kang, M. S., Park, K., et al. (2020) · Food Control · doi:10.1016/j.foodcont.2020.107421 · Cited by 25
Yadav, J., Misra, M., & Singh, K. (2021) · Behaviour and Information Technology · doi:10.1080/0144929x.2021.1872705 · Cited by 25
Counting and locating high-density objects using convolutional neural network
de Arruda, M. D. S., Osco, L. P., Acosta, P. R., Gonçalves, D. N., Marcato, J., Ramos, A. P. M., Matsubara, E. T., Luo, Z., Li, J., Silva, J. D. A., et al. (2022) · Expert Systems with Applications · doi:10.1016/j.eswa.2022.116555 · Cited by 25
Assessing the Performance of Random Forests for Modeling Claim Severity in Collision Car Insurance
Staudt, Y., & Wagner, J. (2021) · Risks · doi:10.3390/risks9030053 · Cited by 25
Misra, I., Rohil, M. K., Moorthi, S. M., & Dhar, D. (2021) · IEEE Transactions on Geoscience and Remote Sensing · doi:10.1109/tgrs.2021.3081768 · Cited by 25
Ao, C., Zeng, W., Wu, L., et al. (2021) · Agricultural Water Management · doi:10.1016/j.agwat.2021.107032 · Cited by 25
Cerfoglio, S., Galli, M., Tarabini, M., Bertozzi, F., Sforza, C., & Zago, M. (2021) · Sensors · doi:10.3390/s21227709 · Cited by 32
Ulpiani, G., Duhirwe, P. N., Yun, G. Y., & Lipson, M. J. (2021) · The Science of The Total Environment · doi:10.1016/j.scitotenv.2021.152537 · Cited by 26
A Comprehensive Review on High-Fidelity and Metamodel-Based Optimization of Composite Laminates
Kalita, K., Haldar, S., & Chakraborty, S. (2022) · Archives of Computational Methods in Engineering · doi:10.1007/s11831-021-09699-z · Cited by 26
Revisiting the Impact of Dependency Network Metrics on Software Defect Prediction
Gong, L., Rajbahadur, G. K., Hassan, A. E., & Jiang, S. (2021) · IEEE Transactions on Software Engineering · doi:10.1109/tse.2021.3131950 · Cited by 25
Yüksel, O., & Köseoğlu, B. (2022) · Ships and Offshore Structures · doi:10.1080/17445302.2022.2028435 · Cited by 27
Wang, B., Chen, T., Li, C., et al. (2022) · Forest Ecology and Management · doi:10.1016/j.foreco.2022.120135 · Cited by 25
LAI-Based Phenological Changes and Climate Sensitivity Analysis in the Three-River Headwaters Region
Dai, X., Fan, W., Shan, Y., et al. (2022) · Remote Sensing · doi:10.3390/rs14153748 · Cited by 25
Markovic, S., Bryan, J. L., Rezaee, R., et al. (2022) · Scientific Reports · doi:10.1038/s41598-022-17886-6 · Cited by 25
A survey of uncover misleading and cyberbullying on social media for public health
Darwish, O., Tashtoush, Y. M., Bashayreh, A., Alomar, A., Alkhaza’leh, S., & Darweesh, D. (2022) · Cluster Computing · doi:10.1007/s10586-022-03706-z · Cited by 26
Ijaz, Z., Zhao, C. B., Ijaz, N., Rehman, Z. U., & Ijaz, A. (2022) · Geocarto International · doi:10.1080/10106049.2022.2138566 · Cited by 25
Predicting soil organic carbon stocks in different layers of forest soils in the Czech Republic
Sarkodie, V. Y. O., Vašát, R., Pouladi, N., et al. (2023) · Geoderma Regional · doi:10.1016/j.geodrs.2023.e00658 · Cited by 25
Sun, Y., Zhang, J., Yu, Z., et al. (2023) · ACS Omega · doi:10.1021/acsomega.3c03247 · Cited by 25
Distribution of CO2 Concentration and Its Spatial Influencing Indices in Urban Park Green Space
Jiang, Y., Liu, Y., Sun, Y., et al. (2023) · Forests · doi:10.3390/f14071396 · Cited by 25
Zaki, M. T., Rowles, L. S., Adjeroh, D., & Orner, K. D. (2023) · ACS ES&T Engineering · doi:10.1021/acsestengg.3c00043 · Cited by 27
Predicting the Productivity of Municipality Workers: A Comparison of Six Machine Learning Algorithms
Bijalwan, P., Gupta, A., Mendiratta, A., Johri, A., & Asif, M. (2024) · Economies · doi:10.3390/economies12010016 · Cited by 42
Exact solution of axial liquid-pipe vibration with time-line interpolation
Xu, Y., & Jiao, Z. (2017) · Journal of Fluids and Structures · doi:10.1016/j.jfluidstructs.2016.12.011 · Cited by 25
Positioning Slow-Moving Platforms by UWB Technology in GPS-Challenged Areas
Toth, C. K., Jóźków, G., Koppányi, Z., & Grejner‐Brzezinska, D. A. (2017) · Journal of Surveying Engineering · doi:10.1061/(asce)su.1943-5428.0000231 · Cited by 25
Drerup, P., Brueck, H., & Scherer, H. W. (2017) · Agricultural Water Management · doi:10.1016/j.agwat.2017.07.010 · Cited by 25
Fu, Q., Hou, R., Li, T., et al. (2018) · Agricultural Water Management · doi:10.1016/j.agwat.2018.10.021 · Cited by 25
Kim, D., Kwon, H., & Han, D. (2019) · Hydrology research · doi:10.2166/nh.2019.127 · Cited by 25
Yaseen, Z. M., Afan, H. A., & Tran, M.-T. (2018) · IOP Conference Series Earth and Environmental Science · doi:10.1088/1755-1315/143/1/012025 · Cited by 25
Kim, S., Alizamir, M., Kim, N. W., et al. (2020) · Sustainability · doi:10.3390/su12229720 · Cited by 25
Metadata
- Authors
- Chai, T., & Draxler, R. R.
- Affiliations
- National Oceanic and Atmospheric Administration (US)
- Venue
- Geoscientific Model Development
- Publisher
- Copernicus GmbH
- Published
- 2014-06-30
- Volume
- 7
- Issue
- 3
- Pages
- 1247-1250
- ISSN
- 1991-959X (ISSN-L)
- 1991-9603
- OpenAlex
- W2102148524
- Semantic Scholar
- 8c42db1839098b46f18265907464c16e49bb7a1c
- Cited by
- 7,178
- References
- 12
- Citations by year
- 2026: 1015 · 2025: 1120 · 2024: 980 · 2023: 873 · 2022: 751 · 2021: 683 · 2020: 538 · 2019: 411 · 2018: 324 · 2017: 235 · 2016: 175 · 2015: 59 · 2014: 13
- FWCI
- 106.31
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- Geoscientific model development (publishedVersion, cc-by)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- Funders
- National Oceanic and Atmospheric Administration (NA09NES4400006)
- Topics
- Physical Sciences › Earth and Planetary Sciences › Atmospheric Science › Meteorological Phenomena and Simulations
- Physical Sciences › Environmental Science › Water Science and Technology › Hydrology and Watershed Management Studies
- Social Sciences › Decision Sciences › Management Science and Operations Research › Forecasting Techniques and Applications
- Keywords
- root mean square error, mean absolute error, model evaluation metrics, error distribution, Gaussian errors, triangle inequality, distance measures, model evaluation, hydrological model evaluation
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
A language model drew the claims from the paper on 2026-10-17, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).
A second model labelled each claim on 2026-10-17 (model jev-1.13-20260917, definition revision gold-guideline-v0.2).
Cited sources are checked with a language model’s help (gpt-6-sol).
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
