{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T06:15:38Z","timestamp":1772172938320,"version":"3.50.1"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1009159","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2021,11,10]],"date-time":"2021-11-10T00:00:00Z","timestamp":1636502400000}}],"reference-count":18,"publisher":"Public Library of Science (PLoS)","issue":"10","license":[{"start":{"date-parts":[[2021,10,29]],"date-time":"2021-10-29T00:00:00Z","timestamp":1635465600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000009","name":"Foundation for the National Institutes of Health","doi-asserted-by":"publisher","award":["R01EY020958-09"],"award-info":[{"award-number":["R01EY020958-09"]}],"id":[{"id":"10.13039\/100000009","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>\n                    The spatial distribution of visual items allows us to infer the presence of latent causes in the world. For instance, a spatial cluster of ants allows us to infer the presence of a common food source. However, optimal inference requires the integration of a computationally intractable number of world states in real world situations. For example, optimal inference about whether a common cause exists based on\n                    <jats:italic>N<\/jats:italic>\n                    spatially distributed visual items requires marginalizing over both the location of the latent cause and 2\n                    <jats:sup>\n                      <jats:italic>N<\/jats:italic>\n                    <\/jats:sup>\n                    possible affiliation patterns (where each item may be affiliated or non-affiliated with the latent cause). How might the brain approximate this inference? We show that subject behaviour deviates qualitatively from Bayes-optimal, in particular showing an unexpected positive effect of\n                    <jats:italic>N<\/jats:italic>\n                    (the number of visual items) on the false-alarm rate. We propose several \u201cpoint-estimating\u201d observer models that fit subject behaviour better than the Bayesian model. They each avoid a costly computational marginalization over at least one of the variables of the generative model by \u201ccommitting\u201d to a point estimate of at least one of the two generative model variables. These findings suggest that the brain may implement partially committal variants of Bayesian models when detecting latent causes based on complex real world data.\n                  <\/jats:p>","DOI":"10.1371\/journal.pcbi.1009159","type":"journal-article","created":{"date-parts":[[2021,10,29]],"date-time":"2021-10-29T13:35:22Z","timestamp":1635514522000},"page":"e1009159","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":0,"title":["Point-estimating observer models for latent cause detection"],"prefix":"10.1371","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7751-4809","authenticated-orcid":true,"given":"Jennifer Laura","family":"Lee","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9835-9083","authenticated-orcid":true,"given":"Wei Ji","family":"Ma","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"340","published-online":{"date-parts":[[2021,10,29]]},"reference":[{"key":"pcbi.1009159.ref001","unstructured":"Von Helmholtz H. Handbuch der physiologischen Optik: mit 213 in den Text eingedruckten Holzschnitten und 11 Tafeln. vol. 9. Voss; 1867."},{"issue":"6870","key":"pcbi.1009159.ref002","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1038\/415429a","article-title":"Humans integrate visual and haptic information in a statistically optimal fashion","volume":"415","author":"MO Ernst","year":"2002","journal-title":"Nature"},{"issue":"9","key":"pcbi.1009159.ref003","doi-asserted-by":"crossref","first-page":"e943","DOI":"10.1371\/journal.pone.0000943","article-title":"Causal inference in multisensory perception","volume":"2","author":"KP K\u00f6rding","year":"2007","journal-title":"PLoS one"},{"issue":"6971","key":"pcbi.1009159.ref004","doi-asserted-by":"crossref","first-page":"244","DOI":"10.1038\/nature02169","article-title":"Bayesian integration in sensorimotor learning","volume":"427","author":"KP K\u00f6rding","year":"2004","journal-title":"Nature"},{"issue":"6","key":"pcbi.1009159.ref005","doi-asserted-by":"crossref","first-page":"1172","DOI":"10.1037\/a0029333","article-title":"A century of Gestalt psychology in visual perception: I. Perceptual grouping and figure\u2013ground organization","volume":"138","author":"J Wagemans","year":"2012","journal-title":"Psychological bulletin"},{"issue":"4","key":"pcbi.1009159.ref006","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1037\/a0039540","article-title":"Bayesian hierarchical grouping: Perceptual grouping as mixture estimation","volume":"122","author":"V Froyen","year":"2015","journal-title":"Psychological Review"},{"issue":"2","key":"pcbi.1009159.ref007","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/0042-6989(93)90156-Q","article-title":"Contour integration by the human visual system: evidence for a local \u201cassociation field\u201d","volume":"33","author":"DJ Field","year":"1993","journal-title":"Vision research"},{"issue":"8","key":"pcbi.1009159.ref008","doi-asserted-by":"crossref","first-page":"1683","DOI":"10.1162\/08997660152469305","article-title":"Orientation, scale, and discontinuity as emergent properties of illusory contour shape","volume":"13","author":"LR Williams","year":"2001","journal-title":"Neural Computation"},{"issue":"5","key":"pcbi.1009159.ref009","doi-asserted-by":"crossref","first-page":"e1002520","DOI":"10.1371\/journal.pcbi.1002520","article-title":"Optimality of human contour integration","volume":"8","author":"UA Ernst","year":"2012","journal-title":"PLoS Comput Biol"},{"issue":"2","key":"pcbi.1009159.ref010","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1016\/j.cognition.2006.03.004","article-title":"From mere coincidences to meaningful discoveries","volume":"103","author":"TL Griffiths","year":"2007","journal-title":"Cognition"},{"issue":"4","key":"pcbi.1009159.ref011","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1017\/S0140525X10003134","article-title":"Bayesian fundamentalism or enlightenment? On the explanatory status and theoretical contributions of Bayesian models of cognition","volume":"34","author":"M Jones","year":"2011","journal-title":"Behavioral and brain sciences"},{"issue":"1","key":"pcbi.1009159.ref012","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1017\/S0952523808080905","article-title":"Bayesian decision theory as a model of human visual perception: testing Bayesian transfer","volume":"26","author":"LT Maloney","year":"2009","journal-title":"Visual neuroscience"},{"issue":"9","key":"pcbi.1009159.ref013","doi-asserted-by":"crossref","first-page":"1170","DOI":"10.1038\/nn.3495","article-title":"Probabilistic brains: knowns and unknowns","volume":"16","author":"A Pouget","year":"2013","journal-title":"Nature neuroscience"},{"issue":"49","key":"pcbi.1009159.ref014","doi-asserted-by":"crossref","first-page":"19060","DOI":"10.1523\/JNEUROSCI.1263-13.2013","article-title":"The irrationality of categorical perception","volume":"33","author":"SM Fleming","year":"2013","journal-title":"Journal of Neuroscience"},{"issue":"1","key":"pcbi.1009159.ref015","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1080\/13546783.2011.650506","article-title":"Reasoning with uncertain categories","volume":"18","author":"GL Murphy","year":"2012","journal-title":"Thinking & Reasoning"},{"issue":"4","key":"pcbi.1009159.ref016","doi-asserted-by":"crossref","first-page":"452","DOI":"10.1037\/rev0000028","article-title":"A detailed comparison of optimality and simplicity in perceptual decision making","volume":"123","author":"S Shen","year":"2016","journal-title":"Psychological review"},{"key":"pcbi.1009159.ref017","doi-asserted-by":"crossref","unstructured":"Heller KA, Ghahramani Z. 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