The DOI matches its Crossref record; 24 of the 24 references it cites were found in a registry or an index.
The Well-Calibrated Bayesian
Abstract
Suppose that a forecaster sequentially assigns probabilities to events. He is well calibrated if, for example, of those events to which he assigns a probability 30 percent, the long-run proportion that actually occurs turns out to be 30 percent. We prove a theorem to the effect that a coherent Bayesian expects to be well calibrated, and consider its destructive implications for the theory of coherence.
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On Software Reliability Models
(1979) · IEEE Transactions on Reliability · doi:10.1109/tr.1979.5220558 · Cited by 2
Genetic algorithms for cross-calibration of categorical data
Aboukhamseen, S. M., & M’Hallah, R. (2017) · Journal of Modern Applied Statistical Methods · doi:10.22237/jmasm/1493599080 · Cited by 2
“Of the numerous criteria that are available to assess probability forecasts, (i.e. validity, refinement, etc.), calibration and scoring rules defined on the probabilities and their subsequently observed outcomes are among the more prevalent methods (Dawid, 1982; Gneiting & Katzfuss, 2014).”
BackgroundMethodBayesian Propensity Score Analysis: Simulation and Case Study.
Kaplan, D. E., & Chen, C. J. S. (2011) · Society for Research on Educational Effectiveness · Cited by 2
A Cardinal Comparison of Experts
Kavaler, I., & Rann Smorodinsky, B. (2020) · Lecture notes in computer science · doi:10.1007/978-3-030-64946-3_29 · Cited by 2
Feinberg, Y., & Lambert, N. S. (2014) · International Journal of Game Theory · doi:10.1007/s00182-014-0423-0 · Cited by 2
Pomatto, L. (2021) · Theoretical Economics · doi:10.3982/te3767 · Cited by 2
“For any possible true law P generating the data, where P is an arbitrary probability measure defined over sequences of outcomes, an expert who predicts according to P will pass the calibration test with high probability Dawid (1982).”
MethodProbability Models in Statistical Data Analysis: Uses, Interpretations, Frequentism-as-Model
Hennig, C. M. (2023) · Springer eBooks · doi:10.1007/978-3-030-19071-2_105-1 · Cited by 5
Boldness-Recalibration for Binary Event Predictions
Guthrie, A. P., & Franck, C. T. (2024) · The American Statistician · doi:10.1080/00031305.2024.2339266 · Cited by 2
“Naturally, calibration is considered a minimal desirable property of predicted probabilities (Dawid 1982).”
Raghavan, M. (2023) · ACM eBooks · doi:10.1145/3603195.3603198 · Cited by 2
“When risk tools are used in practice, a key goal is that they are calibrated: if we look at the set of people who receive a predicted probability of p, we would like a p fraction of the members of this set to be positive instances of the classification problem [11].”
MethodOn Sequences with Non-learnable Subsequences
V'yugin, V. V. (2008) · Springer eBooks · doi:10.1007/978-3-540-79709-8_31 · Cited by 2
Kavaler, I., & Rann Smorodinsky, B. (2019) · Games and Economic Behavior · doi:10.1016/j.geb.2019.08.005 · Cited by 2
“(3) It should be emphasized that reasonableness and error-free are not related notions.”
InfluentialAlgorithmic Monoculture and Social Welfare
Raghavan, M. (2023) · ACM eBooks · doi:10.1145/3603195.3603211 · Cited by 2
Interpreting p-Values and Confidence Intervals Using Well-Calibrated Null Preference Priors
Fay, M. P., Proschan, M. A., Brittain, E., & Tiwari, R. C. (2022) · Statistical Science · doi:10.1214/21-sts833 · Cited by 2
“They showed (see Theorem 3.2) that for one-sided testing of a location shift problem with a symmetric monotone likelihood ratio density and symmetric priors, if the response is in the direction of the alternative hypothesis, then the p-value is equal to the infimum over possible prior distributions of the posterior pr…”
BackgroundResultInfluentialThe True Expert Knows Which Question Should Be AskedPreprint
Dekel, E., & Feinberg, Y. (2004) · SSRN Electronic Journal · doi:10.2139/ssrn.560082 · Cited by 2
“The notion of calibration was suggested by Dawid (1982) for a non-Bayesian nonparametric setting and extensively studied in Dawid (1985).”
MethodRefinement revisited with connections to Bayes error, conditional entropy and calibrated classifiersPreprint
Masnadi-Shirazi, H. (2013) · arXiv (Cornell University) · doi:10.48550/arxiv.1303.2517 · Cited by 2
“n is skilled and trustworthy. In other words it actually rains η = ˆη percent of the time when he predicts the chance of rain is ˆη. It has been argued in DeGroot (1979); DeGroot and Fienberg (1982); Dawid (1982) that a calibrated forecaster is not necessarily a good forecaster or an informative and useful one and tha…”
BackgroundEvaluation of Probabilities: A Level Playing Field?
Winkler, R. L. (1999) · Springer eBooks · doi:10.1007/978-1-4615-5089-1_9 · Cited by 2
Calibration and refinement for classification trees
Fienberg, S. E., & Kim, S. (1998) · Journal of Statistical Planning and Inference · doi:10.1016/s0378-3758(97)00195-x · Cited by 2
Calibration and Bayesian learning
Turdaliev, N. (2002) · Games and Economic Behavior · doi:10.1016/s0899-8256(02)00010-6 · Cited by 2
“The notion of calibration (see Dawid 1982, Foster and Vohra 1997, Kalai et al. 1999, Lehrer 1997) can be used to evaluate the quality of a forecast.”
BackgroundMethodInfluentialA Game-Theoretic Analysis of Updating Sets of ProbabilitiesPreprint
Grünwald, P., & Halpern, J. Y. (2007) · arXiv (Cornell University) · doi:10.48550/arxiv.0711.3235 · Cited by 2
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Chang, C.-L., & Lyuu, Y. (2007) · Lecture notes in computer science · doi:10.1007/978-3-540-73545-8_29 · Cited by 2
Essays in Revealed Preference Theory and Behavioral Economics
Imai, T. (2016) · CaltechTHESIS (California Institute of Technology) · doi:10.7907/z9x63jt5 · Cited by 2
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Bassetti, F., Casarin, R., & Ravazzolo, F. (2015) · SSRN Electronic Journal · doi:10.2139/ssrn.2602465 · Cited by 2
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Gupta, V., Jung, C., Noarov, G., Pai, M. M., & Roth, A. (2021) · RePEc: Research Papers in Economics · doi:10.4230/lipics.itcs.2022.82 · Cited by 19
“In this paper we give techniques for dealing with both of these problems (and similar issues that arise for the problem of predicting label means and higher moments) by drawing on ideas from the literature on calibration [1, 2].”
MethodAccounting for errors in data improves timing in single-cell cancer evolutionPreprint
Chen, K., Moravec, J. C., Gavryushkin, A., Welch, D., & Drummond, A. J. (2021) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2021.03.17.435906 · Cited by 2
“We show our implementation is well-calibrated (Dawid, 1982) and demonstrate the models on both real and simulated single-cell DNA data.”
MethodInfluentialMulti-group Agnostic PAC LearnabilityPreprint
Rothblum, G. N., & Yona, G. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2105.09989 · Cited by 2
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Fong, E., & Holmes, C. C. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2106.06137 · Cited by 2
“However, it is well known that model misspecification can lead Bayesian intervals to be poorly calibrated in the frequentist sense (Dawid, 1982; Fraser et al., 2011), that is the long run proportion of the observed data lying in the (1 − α ) Bayes predictive interval is not necessarily equal to (1 −…”
BackgroundApprochabilité, calibration et regret dans les jeux à observations partielles
Perchet, V. (2010) · HAL · Cited by 2
Ethics in Agricultural Change: Questions and Proposals for Development Processes
Dorward, A. (2008) · The international library of environmental, agricultural and food ethics/The International library of environmental, agricultural and food ethics · doi:10.1007/978-1-4020-8722-6_15 · Cited by 1
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Roth, A., & Shi, M. (2024) · ACM Conference on Economics and Computation (EC) · doi:10.1145/3670865.3673622 · Cited by 1
“The idea of sequential calibration dates to Dawid (1982), and Foster and Vohra (1998) were the first to show that it is possible to maintain calibrated forecasts in a sequential adversarial setting.”
On Calibration in Multi-Distribution Learning
Verma, R., Fischer, V., & Nalisnick, E. (2025) · ACM Conference on Fairness, Accountability, and Transparency (FAccT) · doi:10.1145/3715275.3732060 · Cited by 1
Robust Sensitivity Control in Digital Pathology via Tile Score Distribution Matching
Pignet, A., Klein, J., Robin, G., & Olivier, A. (2025) · Lecture notes in computer science · doi:10.1007/978-3-032-04978-0_54 · Cited by 1
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Jiahao, H., Rahman, M. M. U., & Laleg‐Kirati, T. (2026) · IEEE Sensors Journal · doi:10.1109/jsen.2026.3674940 · Cited by 1
“It involves fine-tuning model parameters to align its outputs with observed real-world data, aiming to minimize discrepancies between predicted outcomes and actual observations [25].”
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King, B. (2026) · PeerJ · doi:10.7717/peerj.21691 · Cited by 1
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Bawden, R. J. (2008) · The international library of environmental, agricultural and food ethics/The International library of environmental, agricultural and food ethics · doi:10.1007/978-1-4020-8722-6_14 · Cited by 1
Introduction: Bayesianism into the 21st Century
Williamson, J., & Corfield, D. (2001) · Applied logic series · doi:10.1007/978-94-017-1586-7_1 · Cited by 1
Bounded rationality and search over small-world models
Laskey, K. B. (1994) · International Journal of Approximate Reasoning · doi:10.1016/0888-613x(94)90023-x · Cited by 1
EFFICIENT TESTING OF FORECASTS
Chang, C.-L., & Lyuu, Y. (2010) · International Journal of Foundations of Computer Science · doi:10.1142/s0129054110007131 · Cited by 1
“A forecaster who knows the distribution of nature can produce well calibrated forecasts [3].”
BackgroundInfluential“World of Uncertainty” Game for Decision-Makers
Kyzy, J. T. (2011) · International Journal of Virtual and Personal Learning Environments · doi:10.4018/jvple.2011040104 · Cited by 1
High-confidence predictions under adversarial uncertainty
Drucker, A. (2012) · Conference on Innovations in Theoretical Computer Science · doi:10.1145/2090236.2090237 · Cited by 1
“1 The second strand of related work is the so-called forecasting problem in decision theory (see [4] for an early, influen-tial discussion).”
BackgroundEnvironmental Ethics and Agricultural Intensification
Palmer, C. (2008) · The international library of environmental, agricultural and food ethics/The International library of environmental, agricultural and food ethics · doi:10.1007/978-1-4020-8722-6_9 · Cited by 1
Does an Efficient Calibrated Forecasting Strategy Exist
Abernethy, J., & Mannor, S. (2011) · Cited by 1
Optimal probabilistic forecasts: When do they work?
Martin, G. M., Loaiza‐Maya, R., Maneesoonthorn, W. O., Frazier, D. T., & Hassan, A. R. (2021) · International Journal of Forecasting · doi:10.1016/j.ijforecast.2021.05.008 · Cited by 2
Learning to Play Equilibria: The Bayesian, Repeated Games Approach∗
Nachbar, J. H. (2004) · Cited by 1
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Raghavan, M. (2023) · ACM eBooks · doi:10.1145/3603195.3603212 · Cited by 1
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Xu, Y., Wu, Y., Li, Y., & Wang, P. (2024) · Annual Reliability and Maintainability Symposium (RAMS) · doi:10.1109/rams51492.2024.10457823 · Cited by 1
“Unlike Bayesian approaches, which may experience poor calibration in the frequentist sense due to model misspecification [17,18], conformal inference provides finite-sample frequentist assurances for predictive intervals.”
BackgroundImprecision in martingale- and test-theoretic prequential randomness
Persiau, F., & de Cooman, G. (2024) · International Journal of Approximate Reasoning · doi:10.1016/j.ijar.2024.109213 · Cited by 1
Investigating Calibrated Classification Scores Through the Lens of Interpretability
Torabian, A., & Urner, R. (2024) · Communications in computer and information science · doi:10.1007/978-3-031-63800-8_11 · Cited by 1
Probability Models in Statistical Data Analysis: Uses, Interpretations, Frequentism-as-Model
Hennig, C. M. (2024) · Springer eBooks · doi:10.1007/978-3-031-40846-5_105 · Cited by 2
Bauer, J. C., Yilmaz, K., Wächter, S., & Daub, R. (2024) · IEEE International Conference on Emerging Technologies and Factory Automation (ETFA) · doi:10.1109/etfa61755.2024.10711012 · Cited by 1
“From such a model, one would expect that for a set of predictions with a confidence of about 0.7, the prediction accuracy is about 70 % [15].”
BackgroundInfluentialPredict to Minimize Swap Regret for All Payoff-Bounded Tasks
Hu, L., & Wu, Y. (2024) · Annual Symposium on Foundations of Computer Science · doi:10.1109/focs61266.2024.00024 · Cited by 1
“Calibration, a notion that originated from the forecasting literature [12], requires the relationship m i = q i n i to hold for every prediction value q i .”
Accounting for Nonrandomly Sampled Data in Nonlinear Regression
Picard, R. R., Hamada, M. S., Hemphill, G., & Hackenberg, R. E. (2015) · Quality Engineering · doi:10.1080/08982112.2014.933979 · Cited by 1
“When the number of data points is small, differences are much greater and (Dawid 1982) there is little that can be done to reduce the harm caused by a poor prior distribution.”
BackgroundAnalysis of the Effectiveness of an Investment Project Using Statistical Bayesian Networks
Voronenko, M. A., Naumov, O., Наумова, Л. М., Topalova, E., Filippova, V. D., & Lytvynenko, V. I. (2020) · International Conference on Advanced Computer Information Technologies (ACIT) · doi:10.1109/acit49673.2020.9208982 · Cited by 1
“For example, in [8,9,10] Shows ways of applying Bayesian network models that were used for business and finance, supporting decision-making in politics and sociology, solving planning problems in management and economics, as well as in medicine for diagnosing various ailments, etc.”
MethodThe Hidden Assumptions Behind Counterfactual Explanations and Principal Reasons
Raghavan, M. (2023) · ACM eBooks · doi:10.1145/3603195.3603204 · Cited by 1
(2008) · Springer eBooks · doi:10.1007/978-1-4020-8817-9_1 · Cited by 1
Agricultural Intensification and the Environment
Busch, L. (2008) · The international library of environmental, agricultural and food ethics/The International library of environmental, agricultural and food ethics · doi:10.1007/978-1-4020-8722-6_10 · Cited by 1
Schmid, A. A. (2008) · The international library of environmental, agricultural and food ethics/The International library of environmental, agricultural and food ethics · doi:10.1007/978-1-4020-8722-6_4 · Cited by 1
Calibration, Expected Utility and Local OptimalityPreprint
Foster, D. P., & Vohra, R. (1999) · RePEc: Research Papers in Economics · Cited by 1
On Calibrated Predictions for Auction Selection MechanismsPreprint
McMahan, H. B., & Muralidharan, O. (2012) · arXiv (Cornell University) · doi:10.48550/arxiv.1211.3955 · Cited by 1
“Much of the earliest work is in the probabilistic forecasting literature [1, 6, 18].”
BackgroundDe Finetti’s Probabilistic Approach and the Theory of Expectations in Economics
Felice, M. D., & Pelloni, G. (1987) · Springer eBooks · doi:10.1007/978-1-4613-1885-9_16 · Cited by 1
Universal Algorithm for Online Trading Based on the Method of CalibrationPreprint
V'yugin, V. V., & Trunov, V. G. (2012) · RePEc: Research Papers in Economics · doi:10.48550/arxiv.1205.3767 · Cited by 1
“A minimal requirement for testing any prediction algorithm is that it should be calibrated (cf. Dawid 1982).”
BackgroundAgricultural Intensification: Some Human Rights Issues
Ouko, J. O. (2008) · The international library of environmental, agricultural and food ethics/The International library of environmental, agricultural and food ethics · doi:10.1007/978-1-4020-8722-6_8 · Cited by 1
Towards a theory of small worlds
Lehner, P. E., & Laskey, K. B. (2002) · Annual Meeting of the North American Fuzzy Information Processing Society (NAFIPS) · doi:10.1109/isuma.1993.366749 · Cited by 1
Prequential probability: game-theoretic = measure theoreticPreprint
Vovk, V. (2009) · arXiv (Cornell University) · doi:10.48550/arxiv.0905.1673 · Cited by 1
Partial Information Framework: Aggregating Estimates from Diverse Information SourcesPreprint
Satopää, V., Jensen, S. T., Pemantle, R., & Ungar, L. (2015) · arXiv (Cornell University) · Cited by 1
Hospital Mortality Rate Estimation for Public ReportingPreprint
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“immediately from Theorem 2.4 and Theorem A.2. 3 Optimal Estimators andProbability Theory 3.1 Calibration From a Bayesian perspective, a good probability assignment should be well calibrated (see e.g. [7]). For example, suppose there are 100 people in a room and you assign each person a probability they are married. If…”
BackgroundInfluentialMasnadi-Shirazi, H. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1704.02578 · Cited by 1
“This idea was expanded upon by later papers such as DeGroot (1979); Dawid (1982) and has been most recently studied under a broader context O’Hagan et al.”
MethodExperiential Learning And Strictly Proper Scoring Rules
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Group calibration is a byproduct of unconstrained learning.Preprint
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Refined approachability algorithms and application to regret minimization with global costsPreprint
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“…and analyzing algorithms for various online decision problems such as regret minimization [Cesa-Bianchi and Lugosi, 2006], asymptotic calibration [Dawid, 1982, Foster and Vohra, 1998], regret minimization with variable stage duration [Mannor and Shimkin, 2008] or with global cost functions…”
MethodCar Accidents and 3G Coverage: New Evidence Using Cell Phone Tower ConstructionPreprint
Hersh, J. S., Lang, B. J., & Lang, M. (2019) · SSRN Electronic Journal · doi:10.2139/ssrn.3437545 · Cited by 1
“According to (Dawid, 1982), forecasts are ”well calibrated if, for example, the long-run proportion of forecast 75 percent credible intervals that succeed in covering the actual value of the predicted quantity turns out to be 75 percent.”
A New Goodness-of-Fit Test for Event Forecasting and its Application to Credit Default ModelsPreprint
Bloechlinger, A., & Leippold, M. (2007) · SSRN Electronic Journal · doi:10.2139/ssrn.821884 · Cited by 1
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Cui, P., Deng, Z., Hu, W., & Zhu, J. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2103.15041 · Cited by 1
“Formally, we say a regressor is well-calibrated (Dawid, 1982; Kuleshov et al., 2018) if for ∀p ∈ [0, 1], the following condition always holds: ∑N i=1 I { yi ≤ F−1 i (p) }”
BackgroundMethodGross, S. T. (2017) · Wiley StatsRef: Statistics Reference Online · doi:10.1002/9781118445112.stat00252.pub2 · Cited by 1
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Wang, H., Liu, A., Yu, Z., Yan, J., Yue, Y., & Anandkumar, A. (2020) · arXiv (Cornell University) · Cited by 1
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Dawid, A. P. (2004) · Encyclopedia of Statistical Sciences · doi:10.1002/0471667196.ess0335 · Cited by 1
Self-citationHowson, C. (2000) · doi:10.1093/0198250371.003.0011 · Cited by 1
(2008) · Springer eBooks · doi:10.1007/978-1-4020-8817-9_2 · Cited by 1
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Picard, R., & Osthus, D. (2022) · medRxiv · doi:10.1101/2022.04.29.22274494 · Cited by 1
“Tendencies for Bayesian applications to be “optimistic with their model assumptions” (Efron, 2005, p. 1) and to “discount the possibility that [they] may be miscalibrated” (Dawid, 1982, p. 606) further exacerbate overconfidence.”
BackgroundWolfson, L. J., & Bousquet, N. (2016) · Wiley StatsRef: Statistics Reference Online · doi:10.1002/9781118445112.stat00231.pub2 · Cited by 1
Mostly CalibratedPreprint
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Dawid, A. P. (2014) · Wiley StatsRef: Statistics Reference Online · doi:10.1002/9781118445112.stat02978 · Cited by 1
Self-citationHowson, C. (2000) · doi:10.1093/0198250371.003.0001 · Cited by 1
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“To validate TnT and ensure that the parameters are well recovered, we performed a well-calibrated study (Dawid 1982).”
MethodBayesian phylodynamics of early vertebrate development in BEAST 2Preprint
Zwaans, A., Seidel, S., Manceau, M., & Stadler, T. (2024) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2024.07.04.601658 · Cited by 1
“We examine the statistical correctness of the likelihood using well-calibrated simulations [49].”
MethodSequential decision making in non-stochastic environments
Bartlett, P. L., & Abernethy, J. (2011)
The verification of probabilistic forecasts in decision and risk analysis
Jose, V. R. R. (2009) · DukeSpace (Duke University)
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Dekel, E., & Feinberg, Y. (2005) · RePEc: Research Papers in Economics
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de Arruda, M. L. (2000) · doi:10.11606/d.45.2000.tde-19072012-112940
Korthals, M. (2008) · The international library of environmental, agricultural and food ethics/The International library of environmental, agricultural and food ethics · doi:10.1007/978-1-4020-8722-6_5
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Romeijn, J., Sterkenburg, T. F., & Grünwald, P. (2012) · Analyse & Kritik · doi:10.1515/auk-2012-0215
“In terms more familiar to statisticians (cf. Dawid 1982), the meta-inductive method needs to be well-calibrated.”
BackgroundComment on Article by Sancetta
Clarke, B. S. (2012) · Bayesian Analysis · doi:10.1214/12-ba701a
“This is important because it seems that the predictive perspective, advocated in statistics at least as early as Dawid (1982), has been becoming more widespread in recent years.”
BackgroundDeGroot, M. H. (2005) · Encyclopedia of Statistical Sciences · doi:10.1002/0471667196.ess2919.pub2
Gani, J. (2014) · Wiley StatsRef: Statistics Reference Online · doi:10.1002/9781118445112.stat03422
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Trunov, V. G., & V'yugin, V. V. (2011) · arXiv (Cornell University) · doi:10.48550/arxiv.1105.4272
Comments on Luis Camacho, “Agriculture Intensification from the Perspective of Development Ethics”
Esquith, S. L. (2008) · The international library of environmental, agricultural and food ethics/The International library of environmental, agricultural and food ethics · doi:10.1007/978-1-4020-8722-6_7
Metadata
- Authors
- Dawid, A. P.
- Affiliations
- University College London (GB)
- Corresponding author
- Dawid, A. P.
- ORCID
- Dawid, A. P.
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 1982-09
- Volume
- 77
- Issue
- 379
- Pages
- 605-610
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W2023943903
- Cited by
- 625
- References
- 24
- Citations by year
- 2026: 22 · 2025: 26 · 2024: 45 · 2023: 51 · 2022: 27 · 2021: 31 · 2020: 39 · 2019: 18 · 2018: 19 · 2017: 15 · 2016: 13 · 2015: 18 · 2014: 23 · 2013: 18 · 2012: 17
- FWCI
- 6.76
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of the American Statistical Association (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Bayesian Modeling and Causal Inference
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Social Sciences › Decision Sciences › Management Science and Operations Research › Forecasting Techniques and Applications
- Keywords
- well calibration, Bayesian forecasting, coherence, subjective probability, Dutch book argument
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.
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 ›
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