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Using Occam's razor and Bayesian modelling to compare discrete and continuous representations in numerosity judgements

Spicer, Jake; Sanborn, Adam N.; Beierholm, Ulrik R.

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Authors

Jake Spicer

Adam N. Sanborn



Abstract

Previous research has established that numeric estimates are based not just on perceptual data but also past experience, and so may be influenced by the form of this stored information. It remains unclear, however, how such experience is represented: numerical data can be processed by either a continuous analogue number system or a discrete symbolic number system, with each predicting different generalisation effects. The present paper therefore contrasts discrete and continuous prior formats within the domain of numerical estimation using both direct comparisons of computational models of this process using these representations, as well as empirical contrasts exploiting different predicted reactions of these formats to uncertainty via Occam’s razor. Both computational and empirical results indicate that numeric estimates commonly rely on a continuous prior format, mirroring the analogue approximate number system, or ‘number sense’. This implies a general preference for the use of continuous numerical representations even where both stimuli and responses are discrete, with learners seemingly relying on innate number systems rather than the symbolic forms acquired in later life. There is however remaining uncertainty in these results regarding individual differences in the use of these systems, which we address in recommendations for future work.

Citation

Spicer, J., Sanborn, A. N., & Beierholm, U. R. (2020). Using Occam's razor and Bayesian modelling to compare discrete and continuous representations in numerosity judgements. Cognitive Psychology, 122, Article 101309. https://doi.org/10.1016/j.cogpsych.2020.101309

Journal Article Type Article
Acceptance Date May 23, 2020
Online Publication Date Jul 3, 2020
Publication Date 2020-11
Deposit Date May 28, 2020
Publicly Available Date Mar 28, 2024
Journal Cognitive Psychology
Print ISSN 0010-0285
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 122
Article Number 101309
DOI https://doi.org/10.1016/j.cogpsych.2020.101309

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