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Cited by 266Multisensory perception and integrationVisual perception and processing mechanismsBayesian Modeling and Causal Inference

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Probability Matching as a Computational Strategy Used in Perception

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Wozny, David R., Beierholm, Ulrik R., Shams, Ladan·2010·PLoS Computational Biology
DOI 10.1371/journal.pcbi.1000871PMC PMC2916852
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Abstract

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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Figure 1 Illustration of the three different decision strategies for producing an auditory estimate of location. (A) A schematic example of sensory representations on a trial with a certain discrepancy between the auditory and visual stimuli. The lightbulb and speaker symbols represent the visual and auditory stimulus locations, respectively. The visual and auditory likelihoods are shown in magenta and blue, respectively. For the sake of simplicity, here we assume that the prior distribution is non-informative (uniform). Therefore, in the case of a common cause (C = 1), i.e., when the two sensory signals are fused to obtain an estimate, a single Gaussian posterior distribution is obtained which is shown in black. The estimate of the location of sound, is the mean of the black distribution. In contrast, in the independent cause scenario (C = 2), this estimate is the mean of the blue distribution. (B) The generative model for the causal inference model. C = 1: One cause can be responsible for both visual and auditory signals, xV and xA. C = 2: Alternatively, two independent causes may generate the visual and auditory cues. The probability of each causal structure can be computed using Bayes' Rule (see Eq. 1). Hypothetical posterior probabilities for the stimuli in (A) are given at the bottom of each causal structure. For model averaging (C), the final auditory estimate would be a weighted average of the two estimates, with each estimate weighted by the probability of its causal structure. For model selection (D), an estimate is derived based on the most probable model, in this case the independent model (C = 2). For probability matching (E), the final auditory estimate in this example would be equal to the independent model estimate (C = 2) 70% of the time, and equal to the common cause model estimate (C = 1) 30% of the time. Visual estimates are produced likewise.
Figure 1 Illustration of the three different decision strategies for producing an auditory estimate of location. (A) A schematic example of sensory representations on a trial with a certain discrepancy between the auditory and visual stimuli. The lightbulb and speaker symbols represent the visual and auditory stimulus locations, respectively. The visual and auditory likelihoods are shown in magenta and blue, respectively. For the sake of simplicity, here we assume that the prior distribution is non-informative (uniform). Therefore, in the case of a common cause (C = 1), i.e., when the two sensory signals are fused to obtain an estimate, a single Gaussian posterior distribution is obtained which is shown in black. The estimate of the location of sound, is the mean of the black distribution. In contrast, in the independent cause scenario (C = 2), this estimate is the mean of the blue distribution. (B) The generative model for the causal inference model. C = 1: One cause can be responsible for both visual and auditory signals, xV and xA. C = 2: Alternatively, two independent causes may generate the visual and auditory cues. The probability of each causal structure can be computed using Bayes' Rule (see Eq. 1). Hypothetical posterior probabilities for the stimuli in (A) are given at the bottom of each causal structure. For model averaging (C), the final auditory estimate would be a weighted average of the two estimates, with each estimate weighted by the probability of its causal structure. For model selection (D), an estimate is derived based on the most probable model, in this case the independent model (C = 2). For probability matching (E), the final auditory estimate in this example would be equal to the independent model estimate (C = 2) 70% of the time, and equal to the common cause model estimate (C = 1) 30% of the time. Visual estimates are produced likewise.CC BY · PubMed Central
Figure 2 Simulated response patterns. Simulated response distributions for the three strategies: model averaging (A), model selection (B), and probability matching (C). Distributions are created from 10,000 samples per condition, using mean subject parameters [σV = 2.5° σA = 10.1° σP = 33.0° pcommon = 0.57], and only changing the decision strategy. Five bimodal conditions are shown for each strategy with the visual stimulus to the far left, and the auditory stimulus growing in discrepancy from the left to the right columns. Vertical blue and magenta dotted lines along with the speaker and lightbulb icons show the true location of the auditory and visual locations, respectively. The predicted log-probability of response is shown by the shaded bars for both the visual (magenta) and auditory (blue) response distributions, with overlaps shown in a darker shade of blue.
Figure 2 Simulated response patterns. Simulated response distributions for the three strategies: model averaging (A), model selection (B), and probability matching (C). Distributions are created from 10,000 samples per condition, using mean subject parameters [σV = 2.5° σA = 10.1° σP = 33.0° pcommon = 0.57], and only changing the decision strategy. Five bimodal conditions are shown for each strategy with the visual stimulus to the far left, and the auditory stimulus growing in discrepancy from the left to the right columns. Vertical blue and magenta dotted lines along with the speaker and lightbulb icons show the true location of the auditory and visual locations, respectively. The predicted log-probability of response is shown by the shaded bars for both the visual (magenta) and auditory (blue) response distributions, with overlaps shown in a darker shade of blue.CC BY · PubMed Central

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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
ORCID
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
DOI
10.1371/journal.pcbi.1000871
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
Licence
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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