# Show Reference: "Probability Matching as a Computational Strategy Used in Perception"

Probability Matching as a Computational Strategy Used in Perception PLoS Computational Biology, Vol. 6, No. 8. (5 August 2010), e1000871, doi:10.1371/journal.pcbi.1000871 by David R. Wozny, Ulrik R. Beierholm, Ladan Shams
@article{wozny-et-al-2010,
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. For any task, the utility function specifies the goal to be achieved. For example, in taking a multiple-choice test, the utility is the total number of correct answers. An optimal decision strategy for a task is one that maximizes the utility. Because the utility functions and decision strategies used in perception have not been empirically investigated, it remains unclear what decision-making strategy is used, and whether the choice of strategy is uniform across individuals and tasks. In this study, we computationally characterize a decision-making strategy for each individual participant in an auditory-visual spatial localization task, where participants need to make implicit inferences about whether or not the auditory and visual stimuli were caused by the same or independent objects. Our results suggest that a) there is variability across individuals in decision strategy, and b) the majority of participants appear to adopt a probability matching strategy that chooses a value according to the inferred probability of that value. These results are surprising, because perception is believed to be highly optimized by evolution, and the probability matching strategy is considered  ” suboptimal” under the commonly assumed utility functions. However, we note that this strategy is preferred (or may be even optimal) under utility functions that value learning.},
author = {Wozny, David R. and Beierholm, Ulrik R. and Shams, Ladan},
day = {5},
doi = {10.1371/journal.pcbi.1000871},
issn = {1553-7358},
journal = {PLoS Computational Biology},
keywords = {auditory, bayes, biology, decision-making, localization, model-averaging, multisensory-integration, probability, probability-matching, visual},
month = aug,
number = {8},
pages = {e1000871+},
pmcid = {PMC2916852},
pmid = {20700493},
posted-at = {2014-05-22 16:05:38},
priority = {2},
publisher = {Public Library of Science},
title = {Probability Matching as a Computational Strategy Used in Perception},
url = {http://dx.doi.org/10.1371/journal.pcbi.1000871},
volume = {6},
year = {2010}
}


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Wozny et al. distinguish between three strategies for multisensory integration: model averaging, model selection, and probability matching.

Wozny et al. found in an audio-visual localization experiment that a majority of their participants' performance was best explained by the statistically sub-optimal probability matching strategy.

Probability matching is a sub-optimal decision strategy, statically, but it can have advantages because it leads to exploration.