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Risk, Unexpected Uncertainty, and Estimation Uncertainty: Bayesian Learning in Unstable Settings
Open accessAbstract
Recently, evidence has emerged that humans approach learning using Bayesian updating rather than (model-free) reinforcement algorithms in a six-arm restless bandit problem. Here, we investigate what this implies for human appreciation of uncertainty. In our task, a Bayesian learner distinguishes three equally salient levels of uncertainty. First, the Bayesian perceives irreducible uncertainty or risk: even knowing the payoff probabilities of a given arm, the outcome remains uncertain. Second, there is (parameter) estimation uncertainty or ambiguity: payoff probabilities are unknown and need to be estimated. Third, the outcome probabilities of the arms change: the sudden jumps are referred to as unexpected uncertainty. We document how the three levels of uncertainty evolved during the course of our experiment and how it affected the learning rate. We then zoom in on estimation uncertainty, which has been suggested to be a driving force in exploration, in spite of evidence of widespread aversion to ambiguity. Our data corroborate the latter. We discuss neural evidence that foreshadowed the ability of humans to distinguish between the three levels of uncertainty. Finally, we investigate the boundaries of human capacity to implement Bayesian learning. We repeat the experiment with different instructions, reflecting varying levels of structural uncertainty. Under this fourth notion of uncertainty, choices were no better explained by Bayesian updating than by (model-free) reinforcement learning. Exit questionnaires revealed that participants remained unaware of the presence of unexpected uncertainty and failed to acquire the right model with which to implement Bayesian updating.
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“Here, deviations from expected uncertainty (“unexpected uncertainty”) should increase learning rates.8,12,13,15–18”
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Cites
Kass, R. E., & Raftery, A. E. (1995) · Journal of the American Statistical Association · doi:10.1080/01621459.1995.10476572 · Cited by 12,558
Nudge: improving decisions about health, wealth, and happiness
(2008) · Choice Reviews Online · doi:10.5860/choice.46-0977 · Cited by 11,624
Knight, F. H. (1921) · Cited by 9,967
“Risk, Ambiguity, and the Savage Axioms.”
Ellsberg, D. (1961) · The Quarterly Journal of Economics · doi:10.2307/1884324 · Cited by 7,891
Statistical Decision Theory and Bayesian Analysis
Berger, J. O. (1985) · Springer Series in Statistics · doi:10.1007/978-1-4757-4286-2 · Cited by 7,722
Rescorla, R. A. (1972) · Medical Entomology and Zoology · Cited by 7,268
Nudge: Improving Decisions About Health, Wealth and Happiness
Adkisson, R. V. (2008) · The Social Science Journal · doi:10.1016/j.soscij.2008.09.003 · Cited by 5,706
Aston-Jones, G., & Cohen, J. D. (2005) · Annual Review of Neuroscience · doi:10.1146/annurev.neuro.28.061604.135709 · Cited by 4,472
Classical conditioning II: Current research and theory.
Black, A. H., & Prokasy, W. F. (1972) · Appleton-Century-Crofts eBooks · Cited by 4,449
Allais, M. (1953) · Econometrica · doi:10.2307/1907921 · Cited by 4,054
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Items 201–265 of 265
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A computational lens on the transdiagnostic nature of intolerance of uncertaintyPreprint
Sandhu, T., Xiao, B., & Lawson, R. P. (2022) · doi:10.31234/osf.io/eug64
Detecting Regime Shifts: Neurocomputational Substrates for Over- and Underreactions to ChangePreprint
Wang, M.-C., Wu, G., & Wu, S. (2023) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2023.05.30.542806 · Cited by 1
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Berrada, T., Bossaerts, P. L., & Ugazio, G. (2024) · SSRN Electronic Journal · doi:10.2139/ssrn.4711883 · Cited by 1
Tuzsus, D., Pappas, I., & Peters, J. (2024) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2024.05.09.593363 · Cited by 1
Decision-making under uncertainty
Bruckner, R., & Nassar, M. R. (2024) · Elsevier eBooks · doi:10.1016/b978-0-12-820480-1.00098-x · Cited by 7
How relevant is the prior? Bayesian causal inference for dynamic perception in volatile environmentsPreprint
Meijer, D., Barumerli, R., & Baumgartner, R. (2024) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2024.10.29.620874 · Cited by 1
Multiple and subject-specific roles of uncertainty in reward-guided decision-makingPreprint
Paunov, A. M., L’Hôtellier, M., Guo, D., He, Z., Yu, A. J., & Meyniel, F. (2024) · eLife · doi:10.7554/elife.103363.1 · Cited by 2
Uncertainty-modulated prediction errors in cortical microcircuitsPreprint
Wilmes, K. A., Petrovici, M. A., Sachidhanandam, S., & Senn, W. (2025) · eLife · doi:10.7554/elife.95127.3 · Cited by 1
Detecting Regime Shifts: Neurocomputational Substrates for Over- and Underreactions to ChangePreprint
Wang, M.-C., Wu, G., & Wu, S. (2025) · eLife · doi:10.7554/elife.104684.1 · Cited by 1
Absence of Systematic Effects of Internalizing Psychopathology on Learning Under UncertaintyPreprint
Satti, M. H., Wille, K., Nassar, M. R., Cichy, R. M., Schuck, N. W., Dayan, P., & Bruckner, R. (2025) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2025.05.12.653409 · Cited by 1
Absence of Systematic Effects of Internalizing Psychopathology on Learning Under UncertaintyPreprint
Satti, M. H., Wille, K., Nassar, M. R., Cichy, R. M., Schuck, N. W., Dayan, P., & Bruckner, R. (2025) · eLife · doi:10.7554/elife.107611.1 · Cited by 1
Essays on Learning and Econometrics
Kayaba, Y. (2013) · doi:10.7907/wf1q-en58
RELPH: A Computational Model for Human Decision Making
Sepahvand, N. M. (2013) · UWSpace (University of Waterloo)
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Falsarone, A. (2016) · Advances in business strategy and competitive advantage book series · doi:10.4018/978-1-5225-1028-4.ch006
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Dunne, S. (2016) · CaltechTHESIS (California Institute of Technology) · doi:10.7907/z9sn06zx
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Li, B., Lan, Y., Guo, W., & Zhao, C. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1804.05170
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Ghambaryan, A., Gutkin, B. S., Klucharev, V. A., & Koechlin, É. (2021) · Frontiers in Neuroscience · doi:10.3389/fnins.2021.704728
Kameda, T., Naito, A., & Masuda, N. (2022) · Research Square · doi:10.21203/rs.3.rs-1230730/v1
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Șandru, A. R. (2022) · Wittgenstein-Studien · doi:10.1515/witt-2022-0010
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Diederich, J., Nawfal, M., Moussawi, N. A., & Tfaily, L. (2018) · PsyArXiv (OSF Preprints) · doi:10.31234/osf.io/uct93
Hsu, M., & Preuschoff, K. (2015) · Elsevier eBooks · doi:10.1016/b978-0-12-397025-1.00260-8
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Falsarone, A. (2018) · IGI Global eBooks · doi:10.4018/978-1-5225-5478-3.ch024
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Tehrani-Safa, A. H., Ghaderi, R., & Sarabi‐Jamab, A. (2023) · PsyArXiv (OSF Preprints) · doi:10.31234/osf.io/yjrdb
Uncertainty-modulated prediction errors in cortical microcircuitsPreprint
Wilmes, K. A., Petrovici, M. A., Sachidhanandam, S., & Senn, W. (2024) · eLife · doi:10.7554/elife.95127.1
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Becker, J., Korn, C. W., & Blank, H. (2024) · Scientific Reports · doi:10.1038/s41598-024-59302-1
Dynamic estimation of the attentional field from visual cortical activity
Bloem, I. M., Bakst, L., McGuire, J. T., & Ling, S. (2025) · eLife · doi:10.7554/elife.104222.3
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Yang, Y., Payzan-LeNestour, É., & Tang, Q. (2024) · SSRN Electronic Journal · doi:10.2139/ssrn.4935465
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Wilmes, K. A., Petrovici, M. A., Sachidhanandam, S., & Senn, W. (2024) · eLife · doi:10.7554/elife.95127.2 · Cited by 1
Disentangling the effects of Anxious, Autistic and Schizotypal Traits on Perceptual InferencePreprint
Bévalot, C., Mallevays, M., de Noyer, E. B., Berkovitch, L., & Meyniel, F. (2024) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2024.10.14.618266
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Zhang, Y., Dam, N. T. V., Ai, H., & Xu, P. (2025) · NeuroImage · doi:10.1016/j.neuroimage.2025.121027
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Meijer, D., Barumerli, R., & Baumgartner, R. (2025) · eLife · doi:10.7554/elife.105385.1 · Cited by 1
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Meijer, D., Barumerli, R., & Baumgartner, R. (2025) · eLife · doi:10.7554/elife.105385 · Cited by 2
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Rich, A., & Gureckis, T. M. (2018) · doi:10.31234/osf.io/pdb83_v1
Author response: Dynamic estimation of the attentional field from visual cortical activity
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Bloem, I. M., Bakst, L., McGuire, J. T., & Ling, S. (2025) · eLife · doi:10.7554/elife.104222.2
Estimation-uncertainty affects decisions with and without learning opportunities
Aberg, K. C., Antle, L., & Paz, R. (2025) · Nature Communications · doi:10.1038/s41467-025-61960-2
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Satti, M. H., Wille, K., Nassar, M. R., Cichy, R. M., Schuck, N. W., Dayan, P., & Bruckner, R. (2025) · eLife · doi:10.7554/elife.107611
Selective Pupil Size Response Within direct and random exploration and exploitation BehaviorsPreprint
Barkay, G., Gabay, S., & Herz, U. (2025) · Research Square · doi:10.21203/rs.3.rs-7740172/v1
He, Z., Yin, Z., & Liu, Y. (2025) · Psychophysiology · doi:10.1111/psyp.70174
Detecting Regime Shifts: Neurocomputational Substrates for Over- and Underreactions to ChangePreprint
Wang, M.-C., Wu, G., & Wu, S. (2025) · eLife · doi:10.7554/elife.104684.2
Blank, H., Korn, C., & Becker, J. (2026) · OSF Preprints (OSF Preprints)
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Findling, C. (2018) · theses.fr (ABES) · doi:10.70675/32e62279zea97z45b1z9326z06a449dae472
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Comay, N. A., Solovey, G., & Barttfeld, P. (2026) · eLife · doi:10.7554/elife.111820
Comay, N. A., Solovey, G., & Barttfeld, P. (2026) · eLife · doi:10.7554/elife.111820.1
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Metadata
- Authors
- Payzan-LeNestour, E., & Bossaerts, P.
- Affiliations
- California Institute of Technology (US)
- ORCID
- Bossaerts, Peter
- Venue
- PLoS Computational Biology
- Publisher
- Public Library of Science (PLoS)
- Published
- 2011-01-20
- Volume
- 7
- Issue
- 1
- Pages
- e1001048
- ISSN
- 1553-734X (ISSN-L)
- 1553-7358
- PMC
- PMC3024253
- OpenAlex
- W2027554764
- Cited by
- 267
- References
- 52
- Citations by year
- 2026: 10 · 2025: 31 · 2024: 24 · 2023: 16 · 2022: 16 · 2021: 18 · 2020: 22 · 2019: 22 · 2018: 19 · 2017: 20 · 2016: 19 · 2015: 18 · 2014: 11 · 2013: 12 · 2012: 8
- FWCI
- 5.59
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Locations
- PLoS Computational Biology (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- Minerva Access (University of Melbourne) (submittedVersion, cc-by)
- CaltechAUTHORS (California Institute of Technology) (submittedVersion, cc-by)
- RePEc: Research Papers in Economics (submittedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- Figshare (submittedVersion, cc-by)
- Infoscience (Ecole Polytechnique Fédérale de Lausanne) (submittedVersion)
- Infoscience (Ecole Polytechnique Fédérale de Lausanne) (submittedVersion, cc-by-nc-nd)
- Funders
- National Science Foundation
- Swiss Finance Institute
- Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung
- Topics
- Social Sciences › Decision Sciences › General Decision Sciences › Decision-Making and Behavioral Economics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Neural and Behavioral Psychology Studies
- Social Sciences › Decision Sciences › Management Science and Operations Research › Advanced Bandit Algorithms Research
- Keywords
- Bayesian learning, restless bandits, risk, estimation uncertainty, ambiguity, structural uncertainty, exploration, learning rate, model-free reinforcement learning, human decision-making, perceived uncertainty, ambiguity aversion
- MeSH terms
- Bayes Theorem, Probability, Risk, Uncertainty
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