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Probability Theory Plus Noise: Descriptive Estimation and Inferential Judgment
Author(s) -
Costello Fintan,
Watts Paul
Publication year - 2018
Publication title -
topics in cognitive science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.191
H-Index - 56
eISSN - 1756-8765
pISSN - 1756-8757
DOI - 10.1111/tops.12319
Subject(s) - frequentist inference , statistics , statistical inference , frequentist probability , normative , noise (video) , bayesian probability , bayes' theorem , statistical model , mathematics , econometrics , psychology , computer science , bayesian inference , artificial intelligence , epistemology , philosophy , image (mathematics)
We describe a computational model of two central aspects of people's probabilistic reasoning: descriptive probability estimation and inferential probability judgment. This model assumes that people's reasoning follows standard frequentist probability theory, but it is subject to random noise. This random noise has a regressive effect in descriptive probability estimation, moving probability estimates away from normative probabilities and toward the center of the probability scale. This random noise has an anti‐regressive effect in inferential judgement, however. These regressive and anti‐regressive effects explain various reliable and systematic biases seen in people's descriptive probability estimation and inferential probability judgment. This model predicts that these contrary effects will tend to cancel out in tasks that involve both descriptive estimation and inferential judgement, leading to unbiased responses in those tasks. We test this model by applying it to one such task, described by Gallistel et al. [Gallistel, C. R., 2014]). Participants' median responses in this task were unbiased, agreeing with normative probability theory over the full range of responses. Our model captures the pattern of unbiased responses in this task, while simultaneously explaining systematic biases away from normatively correct probabilities seen in other tasks.