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

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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
Subjects:	B Philosophy. Psychology. Religion > BF Psychology H Social Sciences > HA Statistics
Divisions:	Faculty of Science > Psychology Faculty of Social Sciences > Warwick Business School
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:	Date Event October 2020 Published 19 March 2020 Available 11 January 2020 Accepted
Volume:	127
Number:	5
Page Range:	pp. 719-748
DOI:	10.1037/rev0000190
Status:	Peer Reviewed
Publication Status:	Published
Publisher Statement:	"©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
RIOXX Funder/Project Grant:	Project/Grant ID RIOXX Funder Name Funder ID 817492-SAMPLING European Research Council http://dx.doi.org/10.13039/501100000781 ES/P008976/1 [ESRC] Economic and Social Research Council http://dx.doi.org/10.13039/501100000269 RP2012-V-022 Leverhulme Trust http://dx.doi.org/10.13039/501100000275 UNSPECIFIED National Institute of Economic and Social Research http://viaf.org/viaf/130181691
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