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The Bayesian sampler : generic Bayesian inference causes incoherence in human probability
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Zhu, Jianqiao, Sanborn, Adam N. and Chater, Nick (2020) The Bayesian sampler : generic Bayesian inference causes incoherence in human probability. Psychological Review, 127 (5). pp. 719-748. doi:10.1037/rev0000190 ISSN 0033-295X.
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Official URL: http://dx.doi.org/10.1037/rev0000190
Abstract
Human probability judgments are systematically biased, in apparent tension with Bayesian models of cognition. But perhaps the brain does not represent probabilities explicitly, but approximates probabilistic calculations through a process of sampling, as used in computational probabilistic models in statistics. Naïve probability estimates can be obtained by calculating the relative frequency of an event within a sample, but these estimates tend to be extreme when the sample size is small. We propose instead that people use a generic prior to improve the accuracy of their probability estimates based on samples, and we call this model the Bayesian sampler. The Bayesian sampler trades off the coherence of probabilistic judgments for improved accuracy, and provides a single framework for explaining phenomena associated with diverse biases and heuristics such as conservatism and the conjunction fallacy. The approach turns out to provide a rational reinterpretation of “noise” in an important recent model of probability judgment, the probability theory plus noise model (Costello & Watts, 2014, 2016a, 2017; Costello & Watts, 2019; Costello, Watts, & Fisher, 2018), making equivalent average predictions for simple events, conjunctions, and disjunctions. The Bayesian sampler does, however, make distinct predictions for conditional probabilities and distributions of probability estimates. We show in 2 new experiments that this model better captures these mean judgments both qualitatively and quantitatively; which model best fits individual distributions of responses depends on the assumed size of the cognitive sample.
Item Type: | Journal Article | |||||||||||||||
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Subjects: | B Philosophy. Psychology. Religion > BF Psychology H Social Sciences > HA Statistics |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Psychology Faculty of Social Sciences > Warwick Business School |
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Library of Congress Subject Headings (LCSH): | Sampling (Statistics), Bayesian statistical decision theory, Adaptability (psychology) | |||||||||||||||
Journal or Publication Title: | Psychological Review | |||||||||||||||
Publisher: | American Psychological Association | |||||||||||||||
ISSN: | 0033-295X | |||||||||||||||
Official Date: | October 2020 | |||||||||||||||
Dates: |
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Volume: | 127 | |||||||||||||||
Number: | 5 | |||||||||||||||
Page Range: | pp. 719-748 | |||||||||||||||
DOI: | 10.1037/rev0000190 | |||||||||||||||
Status: | Peer Reviewed | |||||||||||||||
Publication Status: | Published | |||||||||||||||
Reuse Statement (publisher, data, author rights): | "©American Psychological Association, 2020. This paper is not the copy of record and may not exactly replicate the authoritative document published in the APA journal. Please do not copy or cite without author's permission. The final article is available, upon publication, at: http://dx.doi.org/10.1037/rev0000190 | |||||||||||||||
Access rights to Published version: | Restricted or Subscription Access | |||||||||||||||
Date of first compliant deposit: | 17 January 2020 | |||||||||||||||
Date of first compliant Open Access: | 17 January 2020 | |||||||||||||||
RIOXX Funder/Project Grant: |
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