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Probability Matching as a Computational Strategy Used in Perception
Open accessAbstract
The question of which strategy is employed in human decision making has been studied extensively in the context of cognitive tasks; however, this question has not been investigated systematically in the context of perceptual tasks. The goal of this study was to gain insight into the decision-making strategy used by human observers in a low-level perceptual task. Data from more than 100 individuals who participated in an auditory-visual spatial localization task was evaluated to examine which of three plausible strategies could account for each observer's behavior the best. This task is very suitable for exploring this question because it involves an implicit inference about whether the auditory and visual stimuli were caused by the same object or independent objects, and provides different strategies of how using the inference about causes can lead to distinctly different spatial estimates and response patterns. For example, employing the commonly used cost function of minimizing the mean squared error of spatial estimates would result in a weighted averaging of estimates corresponding to different causal structures. A strategy that would minimize the error in the inferred causal structure would result in the selection of the most likely causal structure and sticking with it in the subsequent inference of location-"model selection." A third strategy is one that selects a causal structure in proportion to its probability, thus attempting to match the probability of the inferred causal structure. This type of probability matching strategy has been reported to be used by participants predominantly in cognitive tasks. Comparing these three strategies, the behavior of the vast majority of observers in this perceptual task was most consistent with probability matching. While this appears to be a suboptimal strategy and hence a surprising choice for the perceptual system to adopt, we discuss potential advantages of such a strategy for perception.
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“Bayesian samplers can match behavioral stochasticity in tasks such as perception, categorization, causal reasoning, and decision making [20,21,23,24].”
From Bayesian Brains without Probabilities (2016) · cites this paper as [23]
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Citations
Cites
Theory of games and economic behavior
Garcia, S. R., & Miller, S. J. (2019) · American Mathematical Society eBooks · doi:10.1090/mbk/121/32 · Cited by 16,777
(1966) · Medical Entomology and Zoology · Cited by 10,293
Signal detection theory and psychophysics
Ingleby, D. (1967) · Journal of Sound and Vibration · doi:10.1016/0022-460x(67)90197-6 · Cited by 8,616
Jeffreys, H., Moran, P. A. P., & Chatfield, C. (1922) · Nature · doi:10.1038/109132a0 · Cited by 7,877
A note on a general definition of the coefficient of determination
NAGELKERKE, N. J. D. (1991) · Biometrika · doi:10.1093/biomet/78.3.691 · Cited by 5,927
The Theory of Games and Economic Behavior
Harrison, R. W., von Neumann, J., & Morgenstern, O. (1945) · Journal of Farm Economics · doi:10.2307/1232672 · Cited by 5,318
Humans integrate visual and haptic information in a statistically optimal fashion
Ernst, M. O., & Banks, M. S. (2002) · Nature · doi:10.1038/415429a · Cited by 4,844
Individual differences in reasoning: Implications for the rationality debate?
Stanovich, K. E., & West, R. F. (2000) · Behavioral and Brain Sciences · doi:10.1017/s0140525x00003435 · Cited by 4,481
The Ventriloquist Effect Results from Near-Optimal Bimodal Integration
Alais, D., & Burr, D. (2004) · Current Biology · doi:10.1016/j.cub.2004.01.029 · Cited by 1,936
Perception as Bayesian Inference
(1996) · doi:10.1017/cbo9780511984037 · Cited by 1,425
Causal Inference in Multisensory Perception
Körding, K. P., Beierholm, U., Ma, W. J., Quartz, S., Tenenbaum, J. B., & Shams, L. (2007) · PLoS ONE · doi:10.1371/journal.pone.0000943 · Cited by 1,069
Self-citationPrécis of Simple heuristics that make us smart
Todd, P. M., & Gigerenzer, G. (2000) · Behavioral and Brain Sciences · doi:10.1017/s0140525x00003447 · Cited by 739
Statistically optimal perception and learning: from behavior to neural representations
Fiser, J., Berkes, P., Orbán, G., & Lengyel, M. (2010) · Trends in Cognitive Sciences · doi:10.1016/j.tics.2010.01.003 · Cited by 672
Theory of games and economic behavior
Neumann, J. V., & Morgenstern, O. (1947) · Virtual Defense Library (Ministerio de Defensa) · Cited by 561
Generation of random sequences by human subjects: A critical survey of literature.
Wagenaar, W. A. (1972) · Psychological Bulletin · doi:10.1037/h0032060 · Cited by 498
On Adaptation, Maximization, and Reinforcement Learning Among Cognitive Strategies.
Erev, I., & Barron, G. (2005) · Psychological Review · doi:10.1037/0033-295x.112.4.912 · Cited by 481
Slant from texture and disparity cues: Optimal cue combination
Hillis, J. M., Watt, S. J., Landy, M. S., & Banks, M. S. (2004) · Journal of Vision · doi:10.1167/4.12.1 · Cited by 421
Do humans optimally integrate stereo and texture information for judgments of surface slant?
Knill, D. C., & Saunders, J. A. (2003) · Vision Research · doi:10.1016/s0042-6989(03)00458-9 · Cited by 415
An Economist’s Perspective on Probability Matching
Vulkan, N. (2000) · Journal of Economic Surveys · doi:10.1111/1467-6419.00106 · Cited by 413
Vision and the statistics of the visual environment
Simoncelli, E. P. (2003) · Current Opinion in Neurobiology · doi:10.1016/s0959-4388(03)00047-3 · Cited by 313
Sound-induced flash illusion as an optimal percept
Shams, L. B., Ma, W. J., & Beierholm, U. (2005) · Neuroreport · doi:10.1097/01.wnr.0000187634.68504.bb · Cited by 281
Towards a model of the mind's eye's movement.
Jonides, J. (1980) · Canadian Journal of Psychology/Revue Canadienne de Psychologie · doi:10.1037/h0081031 · Cited by 274
Bayesian decision theory and psychophysics
Yuille, A. L., & Bülthoff, H. H. (1996) · Perception as Bayesian Inference · doi:10.1017/cbo9780511984037.006 · Cited by 250 · cited 1×
“This strategy in the context of our task translates into model selection [17,18].”
MethodFurther toward a model of the Mind’s eye’s movement
Jonides, J. (1983) · Bulletin of the Psychonomic Society · doi:10.3758/bf03334699 · Cited by 234
The smart potential behind probability matching
Gaissmaier, W., & Schooler, L. J. (2008) · Cognition · doi:10.1016/j.cognition.2008.09.007 · Cited by 223
Roach, N. W., Heron, J., & McGraw, P. V. (2006) · Proceedings of the Royal Society B Biological Sciences · doi:10.1098/rspb.2006.3578 · Cited by 220
Grant, D. A., Hake, H. W., & Hornseth, J. P. (1951) · Journal of Experimental Psychology · doi:10.1037/h0054051 · Cited by 206
Knill, D. C. (2007) · Journal of Vision · doi:10.1167/7.7.5 · Cited by 194
Vision and touch are automatically integrated for the perception of sequences of events
Bresciani, J., Dammeier, F., & Ernst, M. O. (2006) · Journal of Vision · doi:10.1167/6.5.2 · Cited by 183
Human trimodal perception follows optimal statistical inference
Wozny, D. R., Beierholm, U., & Shams, L. B. (2008) · Journal of Vision · doi:10.1167/8.3.24 · Cited by 179
Spatial vision in humans and robots
Harris, L. R., & Jenkin, M. R. M. (1994) · Cited by 155
Interpreting Neural Response Variability as Monte Carlo Sampling of the Posterior
Hoyer, P. O., & Hyvärinen, A. (2002) · Cited by 144
Is probability matching smart? Associations between probabilistic choices and cognitive ability
West, R. F., & Stanovich, K. E. (2003) · Memory & Cognition · doi:10.3758/bf03194383 · Cited by 143
Implicit knowledge of visual uncertainty guides decisions with asymmetric outcomes
Whiteley, L., & Sahani, M. (2008) · Journal of Vision · doi:10.1167/8.3.2 · Cited by 120
Perceptual multistability predicted by search model for bayesian decisions.
Sundareswara, R., & Schrater, P. R. (2008) · Journal of Vision · doi:10.1167/8.5.12 · Cited by 112
TOWARD A UNIFIED THEORY OF DECISION CRITERION LEARNING IN PERCEPTUAL CATEGORIZATION
Maddox, W. T. (2002) · Journal of the Experimental Analysis of Behavior · doi:10.1901/jeab.2002.78-567 · Cited by 109
A Bayesian Model of Conditioned Perception.
Stocker, A. A., & Simoncelli, E. P. (2007) · PubMed · Cited by 98
Attention as inference: Selection is probabilistic; responses are all-or-none samples.
Vul, E., Hanus, D., & Kanwisher, N. (2009) · Journal of Experimental Psychology: General · doi:10.1037/a0017352 · Cited by 86
Searching for Patterns in Random Sequences.
Wolford, G., Newman, S. E., Miller, M. B., & Wig, G. S. (2004) · Canadian Journal of Experimental Psychology / Revue canadienne de psychologie expérimentale · doi:10.1037/h0087446 · Cited by 78
Psychological conceptions of randomness
Ayton, P., Hunt, A. J., & Wright, G. (1989) · Journal of Behavioral Decision Making · doi:10.1002/bdm.3960020403 · Cited by 76
Flow visualization of coaxial jet excited with varying phase differences
Kiwata, T., & Okajimai, A. (2004) · Journal of Visualization · doi:10.1007/bf03181475 · Cited by 68
Probability learning with noncontingent success
Yellott, J. I. (1969) · Journal of Mathematical Psychology · doi:10.1016/0022-2496(69)90023-6 · Cited by 65
Unturbe, J., & Corominas, J. (2007) · Neuropsychology · doi:10.1037/0894-4105.21.5.621 · Cited by 41
Landy, M. S., Goutcher, R., Trommershäuser, J., & Mamassian, P. (2007) · Journal of Vision · doi:10.1167/7.6.4 · Cited by 38
Causal inference in sensorimotor integration
Kording, K. P., & Tenenbaum, J. B. (2007) · The MIT Press eBooks · doi:10.7551/mitpress/7503.003.0097 · Cited by 26
Criteria interactions across visual attributes
Goréa, A., Caetta, F., & Sagi, D. (2005) · Vision Research · doi:10.1016/j.visres.2005.03.018 · Cited by 19
Detectability of low-contrast features in computed tomography
Warren, R. C. (1984) · Physics in Medicine and Biology · doi:10.1088/0031-9155/29/1/001 · Cited by 17
A chance to learn: On matching probabilities to optimize utilities
Burns, K. J., & Demaree, H. A. (2008) · Information Sciences · doi:10.1016/j.ins.2008.11.021 · Cited by 15
Bayesian models, deformable templates and competitive priors
Yuille, A. L., & Clark, J. J. (1994) · Cited by 10
Sampling and Optimal Cue Combination during Bistable Perception
Pouget, A. (2009) · Frontiers in Systems Neuroscience · doi:10.3389/conf.neuro.06.2009.03.098 · Cited by 2
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Bayesian just-so stories in psychology and neuroscience.
Bowers, J. S., & Davis, C. J. (2012) · Psychological Bulletin · doi:10.1037/a0026450 · Cited by 436
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Metadata
- Authors
- Wozny, D. R., Beierholm, U. R., & Shams, L.
- Affiliations
- University of California, Los Angeles (US)
- Gatsby Computational Neuroscience Unit (GB)
- Corresponding author
- Shams, Ladan
- Venue
- PLoS Computational Biology
- Publisher
- Public Library of Science (PLoS)
- Published
- 2010-08-05
- Volume
- 6
- Issue
- 8
- Pages
- e1000871
- ISSN
- 1553-734X (ISSN-L)
- 1553-7358
- PMC
- PMC2916852
- OpenAlex
- W2067064274
- Cited by
- 265
- References
- 50
- Citations by year
- 2026: 14 · 2025: 18 · 2024: 48 · 2023: 15 · 2022: 15 · 2021: 21 · 2020: 15 · 2019: 20 · 2018: 24 · 2017: 18 · 2016: 16 · 2015: 15 · 2014: 5 · 2013: 4 · 2012: 7
- FWCI
- 8.74
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Locations
- PLoS Computational Biology (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- UCL Discovery (University College London) (submittedVersion)
- eScholarship (California Digital Library) (submittedVersion)
- eScholarship (California Digital Library) (submittedVersion, cc-by)
- Max Planck Digital Library (submittedVersion, other-oa)
- Figshare (submittedVersion, cc-by)
- Durham Research Online (Durham University) (submittedVersion, cc-by)
- University of Birmingham Research Portal (University of Birmingham) (submittedVersion, other-oa)
- MPG.PuRe (Max Planck Society) (submittedVersion, other-oa)
- Funders
- National Institutes of Health
- Topics
- Social Sciences › Psychology › Experimental and Cognitive Psychology › Multisensory perception and integration
- Life Sciences › Neuroscience › Cognitive Neuroscience › Visual perception and processing mechanisms
- Physical Sciences › Computer Science › Artificial Intelligence › Bayesian Modeling and Causal Inference
- Keywords
- probability matching, perceptual decision making, causal inference, model selection, weighted averaging, suboptimal strategies, cross-modal integration, perceptual inference
- MeSH terms
- Decision Making, Female, Humans, Male, Probability Learning, Sound Localization, Visual Perception, Young Adult
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