Bayesian inference with incomplete knowledge explains perceptual confidence and its deviations from accuracy
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Abstract
In perceptual decisions, subjects infer hidden states of the environment based on noisy sensory information. Here we show that both choice and its associated confidence are explained by a Bayesian framework based on partially observable Markov decision processes (POMDPs). We test our model on monkeys performing a direction-discrimination task with post-decision wagering, demonstrating that the model explains objective accuracy and predicts subjective confidence. Further, we show that the model replicates well-known discrepancies of confidence and accuracy, including the hard-easy effect, opposing effects of stimulus variability on confidence and accuracy, dependence of confidence ratings on simultaneous or sequential reports of choice and confidence, apparent difference between choice and confidence sensitivity, and seemingly disproportionate influence of choice-congruent evidence on confidence. These effects may not be signatures of sub-optimal inference or discrepant computational processes for choice and confidence. Rather, they arise in Bayesian inference with incomplete knowledge of the environment.
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Self-models may furnish beliefs about the parameters of the confidence formation process, which may not always match the actual parameters of such a process.
“One possibility is that self-models furnish beliefs about the parameters of the confidence formation process (which may not always match the actual parameters of such a process; Fleming & Daw 2017, Khalvati et al. 2021, Marcke et al. 2022).”
From Metacognition and Confidence: A Review and Synthesis (2024) · cites this paper as Khalvati et al. 2021
The Results section on stimulus variability says the decision maker uses a learned observation-noise model for choice and confidence even when it differs from the environment’s true observation noise. That supports the possibility of a parameter mismatch, but the paper does not identify the learned model as a self-model or say that it represents parameters of the confidence-formation process itself. Our copy provides no page numbers for these passages. (LLM, conf=0.82)
Experimental — accuracy not yet measuredDomain-specific limitations may be imposed by how domain-specific uncertainty is propagated into a propositional confidence computation and/or the fidelity of model-based estimates of uncertainty parameters (uncertainty about uncertainty).
“Conversely, domain-specific limitations may be imposed by how domain-specific uncertainty is propagated into a propositional confidence computation and/or the fidelity of model-based estimates of uncertainty parameters (i.e., uncertainty about uncertainty; Boundy-Singer et al. 2023, Khalvati et al. 2021).”
From Metacognition and Confidence: A Review and Synthesis (2024) · cites this paper as Khalvati et al. 2021
The Results section on stimulus variability shows that confidence can be affected when a decision maker uses observation noise learned under one condition in a condition with higher variability. This supports the point about imperfect estimates of uncertainty, but the paper addresses perceptual confidence; it does not establish domain-specific limitations on propositional confidence computations. Page numbers are unavailable in our copy. (LLM, conf=0.82)
Experimental — accuracy not yet measured
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- Authors
- Khalvati, K., Kiani, R., & Rao, R. P. N.
- Affiliations
- University of Washington (US)
- NYU Langone Health (US)
- Corresponding author
- Rao, Rajesh P. N.
- Venue
- Nature Communications
- Published
- 2021-09-29
- Volume
- 12
- Issue
- 1
- Pages
- 5704-5704
- ISSN
- 2041-1723 (ISSN-L)
- PMC
- PMC8481237
- OpenAlex
- W3203924957
- Cited by
- 64
- References
- 79
- Citations by year
- 2026: 5 · 2025: 16 · 2024: 13 · 2023: 17 · 2022: 8 · 2021: 3 · 2020: 2
- FWCI
- 5.39
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Locations
- Nature Communications (publishedVersion, cc-by)
- bioRxiv (Cold Spring Harbor Laboratory) (acceptedVersion, cc-by-nc)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- Funders
- Simons Foundation (542997)
- U.S. Department of Health & Human Services | NIH | National Institute of Mental Health (R01 MH109180-01)
- Alfred P. Sloan Foundation
- McKnight Foundation
- Pew Charitable Trusts
- NSF | ENG/OAD | Division of Engineering Education and Centers (EEC-1028725)
- Templeton World Charity Foundation (TWCF0304)
- Topics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Visual perception and processing mechanisms
- Social Sciences › Decision Sciences › General Decision Sciences › Decision-Making and Behavioral Economics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Neural and Behavioral Psychology Studies
- Keywords
- perceptual confidence, Bayesian inference, partially observable Markov decision processes, perceptual decision making, stimulus variability, direction discrimination, monkeys
- MeSH terms
- Eye-Tracking Technology, Animals, Bayes Theorem, Choice Behavior, Discrimination, Psychological, Macaca, Markov Chains, Models, Psychological, Motion Perception, Photic Stimulation, Reaction Time, Saccades, Models, Animal
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.
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