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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 using expert opinion in ecological analyses: a frequentist approach
Lele, S. R., & Allen, K. L. (2006) · Environmetrics · doi:10.1002/env.786 · Cited by 52
“…of expert opinion has been addressed in the Bayesian literature (Winkler, 1967, 1981; Savage, 1971; French, 1980, 1985, 1986; Kadane et al., 1980; Dawid, 1982, 1987; Kahneman et al., 1982; Lindley, 1983, 1985, 1988; Schervish, 1984; West, 1984, 1988, 1992; Genest and Schervish, 1985; West and…”
BackgroundInferring Ancestral Recombination Graphs from Bacterial Genomic Data
Vaughan, T. G., Welch, D., Drummond, A. J., Biggs, P. J., George, T., & French, N. P. (2016) · Genetics · doi:10.1534/genetics.116.193425 · Cited by 50
“Here we use a well-calibrated (Dawid 1982) form of the test, which requires that known true values fall within the estimated 95% highest posterior density (HPD) interval 95% of the time.”
MethodForecasters’ Objectives and Strategies
Marinovic, I., Ottaviani, M., & Sørensen, P. N. (2013) · Handbook of economic forecasting · doi:10.1016/b978-0-444-62731-5.00012-9 · Cited by 51
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Ripley, B. D. (1994) · Springer eBooks · doi:10.1007/978-3-642-79119-2_5 · Cited by 51
Deterministic Calibration and Nash Equilibrium
Kakade, S. M., & Foster, D. P. (2004) · Lecture notes in computer science · doi:10.1007/978-3-540-27819-1_3 · Cited by 50
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Rakhlin, A., Sridharan, K., & Tewari, A. (2010) · arXiv (Cornell University) · doi:10.48550/arxiv.1011.3168 · Cited by 50
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“Given a network’s prediction ŷ(x) with confidence p̂(x) for a point x, perfect calibration consists of being as likely to be correct as you are confident: p(ŷ = y|p̂ = r) = r, 8r 2 [0, 1] (Dawid, 1982; DeGroot and Fienberg, 1983).”
BackgroundA cautionary note on the discrete uniform prior for the binomial N
Link, W. A. (2013) · Ecology · doi:10.1890/13-0176.1 · Cited by 48
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Wilson, D. J., Crook, D. W., Peto, T., Walker, A. S., Hoosdally, S., Cruz, A. L. G., Carter, J. J., Grazian, C., Earle, S. G., Kouchaki, S., et al. (2020) · Molecular Biology and Evolution · doi:10.1093/molbev/msaa069 · Cited by 45
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Kaplan, D. E., & Chen, J. (2012) · Psychometrika · doi:10.1007/s11336-012-9262-8 · Cited by 46
“Rubin contextualizes his arguments within the notion of the well-calibrated Bayesian (Dawid, 1982). Dawid’s (1982) concept of calibration stems from the notion of forecasting within the Bayesian perspective.2 Dawid uses weather forecasting as an example. Given a weather forecaster’s subjective probability regarding to…”
BackgroundMethodInfluentialUncertainty Quantification for Deep Learning in Ultrasonic Crack Characterization
Pyle, R. J., Hughes, R. R., Ali, A. A. S., & Wilcox, P. D. (2022) · IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control · doi:10.1109/tuffc.2022.3176926 · Cited by 46
“The first is for the UQ method to be “well calibrated” [19].”
Stability and patterns of classroom quality in German early childhood education and care
Kuger, S., Kluczniok, K., Kaplan, D. E., & Rossbach, H.-G. (2015) · School Effectiveness and School Improvement · doi:10.1080/09243453.2015.1112815 · Cited by 48
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BackgroundBayesian Model Comparison and Validation
Geweke, J. F. (2007) · American Economic Review · doi:10.1257/aer.97.2.60 · Cited by 46
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BackgroundBayesian forecasting in economics and finance: A modern review
Martin, G. M., Frazier, D. T., Maneesoonthorn, W. O., Loaiza‐Maya, R., Huber, F., Koop, G. M., Maheu, J. M., Nibbering, D., & Panagiotelis, A. (2023) · International Journal of Forecasting · doi:10.1016/j.ijforecast.2023.05.002 · Cited by 59
“Notable contributions, including some also driven by the criterion of predictive calibration (Dawid, 1982; Dawid, 1985; Gneiting et al., 2007), include Billio et al. (2013), Casarin et al. (2015a), Casarin et al. (2015b), Casarin et al. (2016), Pettenuzzo and Ravazzolo (2016), Aastveit et al.…”
BackgroundRaghavan, M. (2023) · ACM eBooks · doi:10.1145/3603195.3603207 · Cited by 49
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“A well-calibrated simulation study is a powerful tool for evaluating and validating the implementation of a Bayesian model [25].”
MethodCalibrated Bayes, an Alternative Inferential Paradigm for Official Statistics
Little, R. J. A. (2012) · Quality Engineering · Cited by 43
Guo, Y., & Shmaya, E. (2021) · Theoretical Economics · doi:10.3982/te3991 · Cited by 43
“, Dawid (1982), Murphy and Winkler (1987), Ranjan and Gneiting (2010)) for two closely related ideas.”
BackgroundMass estimates for visual binaries with incomplete orbits
Lucy, L. B. (2013) · Astronomy and Astrophysics · doi:10.1051/0004-6361/201322649 · Cited by 43
“One approach to reconciling this aspect of the Bayesian-frequentist debate is that of calibrated Bayes (e.g., Dawid 1982, Little 2006): A credible interval is well-calibrated if the enclosed probability matches the fraction of times that it contains the true value.”
MethodFeinberg, Y., & Stewart, C. (2008) · Econometrica · doi:10.1111/j.1468-0262.2008.00847.x · Cited by 43
Approachability in infinite dimensional spaces
Ehud Lehrer, A. (2003) · International Journal of Game Theory · doi:10.1007/s001820200115 · Cited by 42
“As for approachability in large spaces, Lehrer (2001a) used it to show that there exists a prediction scheme that passes a large set of checking rules a la David (1982).”
MethodApproachability, regret and calibration: Implications and equivalences
Perchet, V. (2014) · Journal of Dynamics and Games · doi:10.3934/jdg.2014.1.181 · Cited by 42
“Obviously, this does not contradict Oakes [57] and Dawid [17] counter-example.”
BackgroundInfluentialThe humble Bayesian: Model checking from a fully Bayesian perspective
Morey, R. D., Romeijn, J., & Rouder, J. N. (2012) · British Journal of Mathematical and Statistical Psychology · doi:10.1111/j.2044-8317.2012.02067.x · Cited by 41
“The applicability of Bayesian quantities will be determined by the quality of the statistical representation, which can be checked using the methods G&S advocate.”
MethodModel averaging for robust extrapolation in evidence synthesis
Röver, C., Wandel, S., & Friede, T. (2018) · Statistics in Medicine · doi:10.1002/sim.7991 · Cited by 40
Bayesian model averaging for harmful algal bloom prediction
Hamilton, G. S., McVinish, R., & Mengersen, K. L. (2009) · Ecological Applications · doi:10.1890/08-1843.1 · Cited by 40
Wenmackers, S., & Romeijn, J. (2015) · Synthese · doi:10.1007/s11229-014-0632-x · Cited by 37
“After all, a standard Bayesian will have the probabilities of the hypotheses under consideration add up to one, and so judges herself to be perfectly calibrated (cf. Dawid 1982).”
BackgroundPower priors based on multiple historical studies for binary outcomes
Gravestock, I., & Held, L. (2018) · Biometrical Journal · doi:10.1002/bimj.201700246 · Cited by 38
“Of note, although there may be increases in type I error probability in some regions of the parameter space, a well-calibrated prior should not have an increase on average over the whole prior distribution (Dawid, 1982).”
BackgroundBayesian Confirmation Theory: Inductive Logic, or Mere Inductive Framework?
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“7 Except in the deterministic case where the hypotheses all entail either the evidence or its negation.”
BackgroundMortality Rate Estimation and Standardization for Public Reporting: Medicare’s Hospital Compare
George, E. I., Ročková, V., Rosenbaum, P. R., Satopää, V. A., & Silber, J. H. (2017) · Journal of the American Statistical Association · doi:10.1080/01621459.2016.1276021 · Cited by 37
“The model is not properly calibrated; see Dawid (1982) for discussion of calibration.”
BackgroundBelot, G. (2013) · Philosophy of Science · doi:10.1086/673249 · Cited by 36
Jampani, V., Nowozin, S., Loper, M., & Gehler, P. (2015) · Computer Vision and Image Understanding · doi:10.1016/j.cviu.2015.03.002 · Cited by 35
“We see that posterior variance is higher in regions of higher error, that is, our model predicts its own uncertainty correctly [13].”
BackgroundSeidel, S., & Stadler, T. (2022) · Proceedings of the Royal Society B Biological Sciences · doi:10.1098/rspb.2022.1844 · Cited by 34
“(b) In silico validation of the implementation We validate TiDeTree using well-calibrated simulations [17]; meaning we draw simulation parameters from a prior distribution and use them to simulate genetic sequences (see electronic supplementary material, appendix A).”
MethodDeterministic calibration and Nash equilibrium
Kakade, S. M., & Foster, D. P. (2007) · Journal of Computer and System Sciences · doi:10.1016/j.jcss.2007.04.017 · Cited by 35
“2 A rather minimal requirement for any prediction algorithm is that it should be calibrated (see [6]).”
BackgroundCalibration of deep probabilistic models with decoupled bayesian neural networks
Maroñas, J., Paredes, R., & Ramos, D. (2020) · Neurocomputing · doi:10.1016/j.neucom.2020.04.103 · Cited by 33
“However, although accuracy is a suitable measure of the performance of DNNs in numerous scenarios, there are many applications in which the probabilities provided by a DNN must be also reliable , i.e. well-calibrated [7].”
BackgroundInfluentialMany inspections are manipulable
Shmaya, E. (2008) · CaltechAUTHORS (California Institute of Technology) · Cited by 33
Strategic Manipulation of Empirical Tests
Olszewski, W., & Sandroni, A. (2009) · Mathematics of Operations Research · doi:10.1287/moor.1080.0347 · Cited by 33
“A proof that the calibration and likelihood tests do not reject the truth with probability one can be found in Dawid (1982, 1985).”
BackgroundBelief Affirming in Learning Processes
Monderer, D., Samet, D., & Sela, A. (1997) · Journal of Economic Theory · doi:10.1006/jeth.1996.2245 · Cited by 33
“Foster and Vohra [4] suggested calibration of the forecasts, in a learning process, as a consistency condition (see Dawid [2]) and showed that in calibrated processes the joint distribution of players' actions converge to the set of correlated equilibria.”
MethodForecasting Software Reliability
Bev Littlewood, A. (1991) · Topics in safety, reliability and quality · doi:10.1007/978-94-011-3482-8_6 · Cited by 33
Multiple Probability Assessments by Dependent Experts
Agnew, C. E. (1985) · Journal of the American Statistical Association · doi:10.1080/01621459.1985.10478120 · Cited by 33
Scoring Rules and Decision Analysis Education
Bickel, J. E. (2010) · Decision Analysis · doi:10.1287/deca.1100.0184 · Cited by 31
“Perhaps more important for Bayesians is the concept of strict coherence , or Cromwell's rule (Dawid 1982, Lindley 1982), which states that a probability of zero should not be assigned to any possibility.”
A Nonmanipulable TestPreprint
Olszewski, W., & Sandroni, A. (2009) · Cited by 30
Inducing Leaders to Take Risky Decisions: Dismissal, Tenure, and Term Limits
Aghion, P., & Jackson, M. O. (2016) · American Economic Journal Microeconomics · doi:10.1257/mic.20150083 · Cited by 31
Calibration, Sufficiency, and Domination Considerations for Bayesian Probability Assessors
Vardeman, S. B., & Meeden, G. D. (1983) · Journal of the American Statistical Association · doi:10.1080/01621459.1983.10477025 · Cited by 31
Calibrated lazy associative classification
Veloso, A., Meira, W., Gonçalves, M., Almeida, H. M., & Zaki, M. (2010) · Information Sciences · doi:10.1016/j.ins.2010.03.007 · Cited by 30
“1 The notion of calibration (sometimes termed reliability), was introduced in [6] to describe situations where the observed frequencies of events match the probabilities forecasted for them.”
Loaiza‐Maya, R., Martin, G. M., & Frazier, D. T. (2021) · Journal of Applied Econometrics · doi:10.1002/jae.2810 · Cited by 30
Evaluating probability forecasts
Lai, T. L., Gross, S. T., & Shen, D. B. (2011) · The Annals of Statistics · doi:10.1214/11-aos902 · Cited by 28
“essed this issue by using pi = EΠ(Yi|Gi−1) under the null hypothesis H0 that assumes the sequence of events are generated by the probability measure Π. This approach is related to the earlier work of Dawid (1982), who assumes a “subjective probability distribution” Π for the events so that Bayesian forecasts are given…”
MethodResultInfluentialInconsistency of Bayesian Inference for Misspecified Linear Models, and a Proposal for Repairing It
Grünwald, P., & van Ommen, T. (2017) · Bayesian Analysis · doi:10.1214/17-ba1085 · Cited by 37
“This is done via Dawid’s (1984) prequential view on Bayesian inference.”
MethodThe assessment of replication success based on relative effect size
Held, L., Micheloud, C., & Pawel, S. (2022) · The Annals of Applied Statistics · doi:10.1214/21-aoas1502 · Cited by 36
“Although Bayesian methods do not rely on the frequentist paradigm of repeated testing, it is still useful to investigate their frequentist operating characteristics (Dawid, 1982; Rubin, 1984; Grieve, 2016) and this also holds for the proposed reverse-Bayes assessment of replication success.”
MethodOn optimal sequential prediction for general processes
Nobel, A. B. (2003) · IEEE Transactions on Information Theory · doi:10.1109/tit.2002.806141 · Cited by 29
Metacognitive Information Theory
Dayan, P. (2023) · Open Mind · doi:10.1162/opmi_a_00091 · Cited by 34
“be metacognitively unbiased if she reported the correct overall probability of being correct on every trial, independent of the actual observation (like a well-calibrated, but useless, weather forecaster reporting on every day of the year, the overall mean probability of rain; Dawid, 1982).”
A Score Regression Approach to Assess Calibration of Continuous Probabilistic Predictions
Held, L., Rufibach, K., & Balabdaoui, F. (2010) · Biometrics · doi:10.1111/j.1541-0420.2010.01406.x · Cited by 27
“Good calibration is a central requirement for probabilistic predictions, both from a frequentist (Cox, 1958; Butler, 1986) and a Bayesian (Dawid, 1982) perspective.”
BackgroundMethodAn axiomatic characterization of wagering mechanisms
Lambert, N. S., Langford, J., Vaughan, J. W., Chen, Y.-L., Reeves, D. M., Shoham, Y., & Pennock, D. M. (2015) · Journal of Economics Theory · doi:10.1016/j.jet.2014.03.012 · Cited by 30
“1 It is common in the forecasting literature to assume outcomes are drawn at random from some true, objective probability distribution [7,11,34].”
BackgroundThe Sceptical Bayes Factor for the Assessment of Replication Success
Pawel, S., & Held, L. (2022) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/rssb.12491 · Cited by 30
“3 Frequentist properties Despite the fact that Bayesian methods do not rely on repeated testing, it is still often of interest to study their frequentist operating characteristics (Dawid, 1982; Grieve, 2016).”
BackgroundAn information theoretic approach to reducing algorithmic bias for machine learning
Kim, J.-Y., & Cho, S. (2022) · Neurocomputing · doi:10.1016/j.neucom.2021.09.081 · Cited by 31
Further thoughts on testing for causality with econometric models
Swamy, P. A. V. B., & Muehlen, P. V. Z. (1988) · Journal of Econometrics · doi:10.1016/0304-4076(88)90042-5 · Cited by 27
Stable Discovery of Interpretable Subgroups via Calibration in Causal Studies
Dwivedi, R., Yan, T., Park, B., Wei, M., Horgan, K., Madigan, D., & Yu, B. (2020) · International Statistical Review · doi:10.1111/insr.12427 · Cited by 31
“Related ideas have been used to calibrate a wide range of methods, including Bayesian models (Dawid, 1982), support vector machines, boosted trees, RFs (Niculescu-Mizil & Caruana, 2005; Naeini et al., 2015) and more recently deep neural networks (Guo et al., 2017).”
BackgroundMethodInfluentialCalculating LRs for presence of body fluids from mRNA assay data in mixtures
Ypma, R. J. F., van Wijk, P. A. M., Gill, R. D., Sjerps, M. J., & van den Berge, M. (2021) · Forensic Science International Genetics · doi:10.1016/j.fsigen.2020.102455 · Cited by 26
“Equivalently, in a forensic context, for well-calibrated systems the property ‘the LR is the LR of the LR’ holds [31,32].”
BackgroundLyu, M. R.-T., & Nikora, A. P. (2002) · Proceedings/Proceedings - International Symposium on Software Reliability Engineering · doi:10.1109/issre.1991.145376 · Cited by 26
Ilias, L., & Askounis, D. (2023) · Knowledge-Based Systems · doi:10.1016/j.knosys.2023.110834 · Cited by 26
“In addition, the reliability of a machine learning model’s confidence in its predictions, denoted as calibration [14, 49], is critical for high risk applications, such as deciding whether to trust a medical diagnosis prediction [12, 29, 62].”
BackgroundAssessing Generalization of SGD via DisagreementPreprint
Jiang, Y., Nagarajan, V., Baek, C., & Kolter, J. Z. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2106.13799 · Cited by 75
“Calibration of a statistical model is the property that the probability obtained by the model reflects the true likelihood of the ground truth (Murphy & Epstein, 1967; Dawid, 1982).”
BackgroundRodríguez-Pérez, J., Andreu-Martínez, R., Daza, R., Fernández-Arroyo, L., Hernández-García, A., Díaz‐García, E., Cubillos‐Zapata, C., Lozano-Díez, A., Morales, A., Ramos, D., et al. (2025) · Antioxidants · doi:10.3390/antiox14070839 · Cited by 29
“However, the utility of these models depends on their calibration, as misaligned probabilities can lead to harmful over-or underestimations that may affect treatment, diagnosis, or prognosis [344,345].”
Evaluating large language models for accuracy incentivizes hallucinations
Kalai, A. T., Nachum, O., Vempala, S., & Zhang, E. (2026) · Nature · doi:10.1038/s41586-026-10549-w · Cited by 730
Heuristic stopping rules for technology-assisted review
Yang, E., Lewis, D. D., & Frieder, O. (2021) · ACM Symposium on Document Engineering (DocEng) · doi:10.1145/3469096.3469873 · Cited by 24
“, that if one took a large sample of documents with predicted probability pi , it would contain a fraction pi of relevant documents [10].”
BackgroundExcess Ground Ice Profiles in Continuous Permafrost Mapped From InSAR Subsidence
Zwieback, S., Iwahana, G., Sakhalkar, S., Biessel, R., Taylor, S., & Meyer, F. J. (2024) · Water Resources Research · doi:10.1029/2023wr035331 · Cited by 23
“Theory predicts a coverage of 80%, as the simulated truth was drawn from the prior distribution (Dawid, 1982).”
BackgroundTools for the Analysis of the Accuracy of Software Reliability Predictions
Bev Littlewood, A., Ghaly, A. A. A., & Chan, P. Y. (1986) · Springer eBooks · doi:10.1007/978-3-642-82846-1_10 · Cited by 22
Toward estimation of map accuracy without a probability test sample
Steele, B. M., Patterson, D. A., & Redmond, R. L. (2003) · Environmental and Ecological Statistics · doi:10.1023/a:1025111108050 · Cited by 22
“Dawid (1982), Cox (1958), and Ripley (1996, Chap.”
Internal Regret with Partial Monitoring. Calibration-Based Optimal AlgorithmsPreprint
Perchet, V. (2011) · arXiv (Cornell University) · doi:10.48550/arxiv.1102.4442 · Cited by 22
“Perchet [24] provided an alternative algorithm, recalled in section 2.2; this latter is based on calibration, a notion introduced by Dawid [12].”
BackgroundMethodInfluentialUncertainty Quantification for Sparse Deep LearningPreprint
Wang, Y., & Ročková, V. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2002.11815 · Cited by 22
“Our work sheds light on the fact that frequentist calibration is an attainable goal of Bayesian statistical procedures, where the BvM phenomenon facilitates communication of uncertainty us-ing the more universally understood frequentist concept (Dawid, 1982).”
BackgroundAN INVESTIGATION OF THE VALIDITY OF AN EMPIRICAL BAYES APPROACH TO MANTEL‐HAENSZEL DIF ANALYSIS
Zwick, R., Thayer, D. T., & Lewis, C. (1997) · ETS Research Report Series · doi:10.1002/j.2333-8504.1997.tb01742.x · Cited by 21
A New Goodness-of-Fit Test for Event Forecasting and Its Application to Credit Defaults
Blöchlinger, A., & Leippold, M. (2011) · Management Science · doi:10.1287/mnsc.1100.1283 · Cited by 21
“To derive our new test statistic, we operationalize Dawid’s (1982) definition by introducing two components: level calibration and shape calibration.”
Accounting for Errors in Data Improves Divergence Time Estimates in Single-cell Cancer Evolution
Chen, K., Moravec, J. C., Gavryushkin, A., Welch, D., & Drummond, A. J. (2022) · Molecular Biology and Evolution · doi:10.1093/molbev/msac143 · Cited by 20
“First, we evaluated our implementations using a well-calibrated study (Dawid 1982) to test the reliability of the inference when simulating directly from the model.”
Limit theorems for empirical processes based on dependent data
Berti, P., Pratelli, L., & Rigo, P. (2012) · Electronic Journal of Probability · doi:10.1214/ejp.v17-1765 · Cited by 20
Switching Supervisory Control Using Calibrated Forecasts
Al‐Shyoukh, I., & Shamma, J. S. (2009) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2009.2014923 · Cited by 20
“A calibrated forecast [5], [9] guarantees that forecasts are “consistent” in hindsight.”
BackgroundGrünwald, P. (2011) · Cited by 20
Calibration and Expert Testing
Olszewski, W. (2014) · Handbook of game theory and economic applications · doi:10.1016/b978-0-444-53766-9.00018-5 · Cited by 20
Probability, Symmetry and Frequency
Dawid, A. P. (1985) · The British Journal for the Philosophy of Science · doi:10.1093/bjps/36.2.107 · Cited by 20
Self-citationComputing Bayes: Bayesian Computation from 1763 to the 21st CenturyPreprint
Martin, G. M., Frazier, D. T., & Robert, C. P. (2020) · arXiv (Cornell University) · doi:10.26180/21529302 · Cited by 20
FNNC: Achieving Fairness through Neural NetworksPreprint
Padala, M., & Gujar, S. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1811.00247 · Cited by 20
“[Dawid, 1982] A.”
BackgroundDawid, A. P. (2005) · Encyclopedia of Statistical Sciences · doi:10.1002/0471667196.ess2064.pub2 · Cited by 20
Self-citationThe Externalities of Exploration and How Data Diversity Helps Exploitation
Raghavan, M. (2023) · ACM eBooks · doi:10.1145/3603195.3603208 · Cited by 20
Olszewski, W., & Sandroni, A. (2009) · The Annals of Statistics · doi:10.1214/08-aos597 · Cited by 19
“A prequential test rejects or accepts a theory based only on the observed data sequence and the next period forecasts made by the theory along the realized sequence of outcomes [see Dawid (1991) for more details on the prequential principle].”
BackgroundInfluentialVergeer, P., van Schaaik, Y., & Sjerps, M. J. (2021) · Forensic Science International · doi:10.1016/j.forsciint.2021.110722 · Cited by 19
Grünwald, P. (2017) · Journal of Statistical Planning and Inference · doi:10.1016/j.jspi.2017.09.014 · Cited by 27
Conformal Decision Theory: Safe Autonomous Decisions from Imperfect Predictions
Lekeufack, J., Angelopoulos, A. N., Bajcsy, A., Jordan, M. I., & Malik, J. (2024) · 2024 IEEE International Conference on Robotics and Automation (ICRA) · doi:10.1109/icra57147.2024.10610041 · Cited by 18
“This is commonly known as the adversarial sequence model [10], [38].”
BackgroundKaplan, D. E., Chen, J., Yavuz, S., & Lyu, W. (2022) · Psychometrika · doi:10.1007/s11336-022-09869-3 · Cited by 20
“A relatively recent dynamic version of the power prior was considered by Liu (2018), in which the power prior parameter is a continuous function of the p-value used to test the null hypothesis that the current data are equivalent to the historical data. Evenmore recently, Thompson et al. (2021) demonstrated another ty…”
MethodInfluentialWell Calibrated, Coherent Forecasting Systems
Berti, P., Regazzini, E., & Rigo, P. (1998) · Theory of Probability and Its Applications · doi:10.1137/s0040585x97975988 · Cited by 18
Statistical Decision Problems and Bayesian Nonparametric Methods
Gutiérrez‐Peña, E., & Walker, S. G. (2006) · International Statistical Review · doi:10.1111/j.1751-5823.2005.tb00151.x · Cited by 18
“So while authors such as Box (1980) and Dawid (1982) seem to believe that some measure of incoherence is inevitable, here we show how one can undertake parametric inference, in its widest sense, without behaving irrationally.”
BackgroundSelection Problems in the Presence of Implicit Bias
Raghavan, M. (2023) · ACM eBooks · doi:10.1145/3603195.3603209 · Cited by 21
Distribution-free binary classification: prediction sets, confidence intervals and calibrationPreprint
Gupta, C., Podkopaev, A., & Ramdas, A. (2020) · Neural Information Processing Systems · doi:10.48550/arxiv.2006.10564 · Cited by 106
“Murphy and Epstein [31] described the ideal notion of calibration, called perfect calibration (2), which has also been referred to as calibration in the small [45], or sometimes simply as calibration [7, 12, 44].”
BackgroundAgriculture Intensification from the Perspective of Development Ethics
Camacho, 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_6 · Cited by 17
Shafer, G. R. (1990) · Springer eBooks · doi:10.1007/978-94-015-7873-8_5 · Cited by 17
Expert opinion and probabilistic volcanic risk assessment
Donovan, A. R., Eiser, J. R., & Sparks, R. S. J. (2015) · Journal of Risk Research · doi:10.1080/13669877.2015.1115425 · Cited by 17
“The comparison of probabilities obtained from frequency analysis and those obtained from belief-based analysis is not conceptually meaningful (Dawid, 1982; Hacking, 2001) for a single event (though beliefbased analysis may take frequencies into account).”
MethodBayesian probabilistic forecasting with large-scale educational trend data: a case study using NAEP
Kaplan, D. E., & Huang, M. (2021) · Large-scale Assessments in Education · doi:10.1186/s40536-021-00108-2 · Cited by 17
“Specifically, BMA-based models are better calibrated to actual outcomes than any single model that one would choose, and the principle of choosing well-calibrated forecasting models is a key goal of predictive modeling (Dawid, 1982). Below, we will employ two specific scoring rules that we will use to evaluate the pre…”
BackgroundMethodInfluentialJudgmental forecasting of univariate time series
Harvey, N. (1988) · Journal of Behavioral Decision Making · doi:10.1002/bdm.3960010204 · Cited by 17
Forecasting Performance of an Open Economy Dynamic Stochastic General Equilibrium ModelPreprint
Malin Adolfson, A., Lindé, J., & Villani, M. (2005) · RePEc: Research Papers in Economics · Cited by 17
Predictive Likelihood Comparisons with DSGE and DSGE-VAR ModelsPreprint
Warne, A., Coenen, G., & Christoffel, K. P. (2013) · SSRN Electronic Journal · doi:10.2139/ssrn.2250968 · Cited by 15
“Their evaluation scheme is therefore related to the idea of predictive checks (see, e.g., Geweke, 2005) and the idea of examining whether the predictive distribution of the model is, using the terminology of Dawid (1982), “well calibrated”.”
BackgroundMethodInfluentialCalibration and Uncertainty in Neural Time-to-Event Modeling
Chapfuwa, P., Tao, C., Li, C., Khan, I., Chandross, K. J., Pencina, M. J., Carin, L., & Henao, R. (2020) · IEEE Transactions on Neural Networks and Learning Systems · doi:10.1109/tnnls.2020.3029631 · Cited by 16
“Calibration, also known as reliability [28] in Bayesian analysis, is a statistical concept that refers to the consistency (in distribution) of estimates relative to (population-wide) observed measurements, e.g., event times.”
BackgroundVergeer, P. (2023) · Law Probability and Risk · doi:10.1093/lpr/mgad005 · Cited by 16
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
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