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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Cites
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Cited by
Sorted by citations
Items 601–618 of 618
Individualized Forecasting of Headache Attack Risk Using a Continuously Updating ModelPreprint
Houle, T. T., Lebowitz, A. D., Chtay, I., Patel, T., McGeary, D. D., & Turner, D. P. (2026) · medRxiv · doi:10.64898/2026.04.20.26350119
Medical findings in young patients with head trauma: How strong is the evidence for abuse?
Hymel, K. P., Sjerps, M. J., & Vergeer, P. (2026) · International Journal of Legal Medicine · doi:10.1007/s00414-026-03831-z
“However, it is also important to study calibration [8], because the evidential value of medical findings should not be over-or under-estimated.”
Schmaltz, A. (2026) · ACM Conference on AI and Agentic Systems (CAIS) · doi:10.1145/3786335.3813214
“…estimates of the predictive uncertainty for selective classification [5, 10, inter alia], but class-and prediction-conditional calibration in high-probability regions is not a quantity typically targeted by existing classes of calibration methods [1, 4, 6, 9, 21, 22, 28, 35, 36, inter alia].”
Raychev, S. (2026) · International Journal of Systems Science · doi:10.1080/00207721.2026.2681134
MCMC and Particle Filtering for Dynamic INAR Processes
Soyer, R., Lopes, H. F., & Zhang, D. (2026) · Applied Stochastic Models in Business and Industry · doi:10.1002/asmb.70104
Kondam, K. V. R. (2026) · International Symposium of Systems, Advanced Technologies and Knowledge (ISSATK) · doi:10.1109/issatk69667.2026.11566958
“…denote true redshift for galaxy i , ˆ z i a point estimate, and p i ( z ) the estimated PDF. Point-estimate metrics: PDF calibration metrics: • Probability integral transform (PIT) histogram [19]: For each galaxy, compute u i = If PDFs are perfectly calibrated, { u i } should be uniform U (0 , 1) .”
Evaluating Model Performance and Fairness without Labeled Representative Data
van der Laan, E., Tollenaar, N., Barros, A. I., & Snoek, L. (2026) · ACM Conference on Fairness, Accountability, and Transparency (FAccT) · doi:10.1145/3805689.3812303
“A key case in which model-implied outcome information is sufficient, arises when the model is well-calibrated, i.e., when E [ 𝑌 | ˆ 𝑌 = 𝑠,𝐴 ] = 𝑠 [4, 14].”
Cao, D. (2026) · SSRN Electronic Journal · doi:10.2139/ssrn.7049119
Evidence That Settles, Evidence That SteersPreprint
Mayoh, A. (2026) · SSRN Electronic Journal · doi:10.2139/ssrn.7210019
Idrees, M., Al-Obeidat, F. N., & Amin, A. (2026) · Procedia Computer Science · doi:10.1016/j.procs.2026.08.413
Hong, T., Zhang, B., Yao, X., Guo, Z., & Xie, G. (2026) · Sensors · doi:10.3390/s26206600
Calibration Results for Established Post-hoc Calibration Methods
Huang, W. (2025) · Zenodo (CERN European Organization for Nuclear Research) · doi:10.5281/zenodo.15868156
Pre-Adaptation and Confidence Calibration in Synthetic Environments
Ray, A. (2026) · Oxford University Press eBooks · doi:10.1093/9780198945215.003.0285
Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles
Lakshminarayanan, B., Pritzel, A., & Blundell, C. (2016) · arXiv · doi:10.48550/arxiv.1612.01474 · Cited by 3,666
“Firstly, we shall examine calibration [12, 13], a frequentist notion of uncertainty which measures the discrepancy between subjective forecasts and (empirical) long-run frequencies.”
MethodMeasuring Calibration in Deep Learning
Nixon, J., Dusenberry, M., Jerfel, G., Nguyen, T., Liu, J., Zhang, L., & Tran, D. (2019) · arXiv · doi:10.48550/arxiv.1904.01685 · Cited by 209
“One mathematical formulation of the reliability of confidence is calibration (Murphy and Epstein, 1967; Dawid, 1982).”
BackgroundBeing Bayesian about Categorical Probability
Joo, T., Chung, U., & Seo, M.-G. (2020) · arXiv · doi:10.48550/arxiv.2002.07965 · Cited by 37
“Specifically, we measure the calibration performance on in-distribution test samples, which examines a model’s ability to match its probabilistic output associated with an event to the actual long-term frequency of the event (Dawid, 1982).”
BackgroundCalibrated Reliable Regression using Maximum Mean Discrepancy
Cui, P., Hu, W., & Zhu, J. (2020) · arXiv · doi:10.48550/arxiv.2006.10255 · Cited by 27
“Formally, we define a well-calibrated regressor [12, 22] if the following condition holds, for all p ∈ [0, 1], ∑N i=1 I { yi ≤ F−1 i (p) }”
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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