{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,11]],"date-time":"2026-08-11T18:32:13Z","timestamp":1786473133129,"version":"build-2736575974"},"reference-count":36,"publisher":"Public Library of Science (PLoS)","issue":"8","license":[{"start":{"date-parts":[[2026,8,11]],"date-time":"2026-08-11T00:00:00Z","timestamp":1786406400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000181","name":"Air Force Office of Scientific Research","doi-asserted-by":"publisher","award":["FA9550-19-1-0411"],"award-info":[{"award-number":["FA9550-19-1-0411"]}],"id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000879","name":"Alfred P. Sloan Foundation","doi-asserted-by":"publisher","award":["G-2024-22395"],"award-info":[{"award-number":["G-2024-22395"]}],"id":[{"id":"10.13039\/100000879","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.plosone.org"],"crossmark-restriction":false},"short-container-title":["PLoS One"],"abstract":"<jats:p>Biological organisms have sensors that communicate information about the environment. Analyzing how well these biological sensors function has usually been done with mutual information between the sensor signal and the environment, but that can be computationally intractable and summarize something quite complex with just a single number. We suggest that alternatively, one may profitably analyze these biosensors using bias and variance or confusion matrices, depending on the kind of environment. Stimulus-dependent Maximum Entropy models are used to develop estimators of the environmental state given the sensor state, and these estimators in turn are then used to calculate either the bias and variance of the estimator or confusion matrices. We focus on several examples to understand the utility of non-information-based analyses: ligand-receptor binding models spanning from genetic regulation to neuronal communication to bacterial chemotaxis and spin-glass Ising models for neural activity in cultured neurons. These new computationally efficient analyses add insight into existing analyses based on mutual information; in particular, mutual information estimates give one number to characterize responses to all environmental inputs, and this analysis method characterizes how sensors respond to each environmental input. Categorical analyses, meanwhile, indicate the presence of memory without much prediction in confusion matrix elements in cultured neural networks, adding to previous understanding from mutual information estimates.<\/jats:p>","DOI":"10.1371\/journal.pone.0342165","type":"journal-article","created":{"date-parts":[[2026,8,11]],"date-time":"2026-08-11T17:39:05Z","timestamp":1786469945000},"page":"e0342165","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":0,"title":["Analyzing an organism\u2019s sensors using Maximum Entropy (MaxEnt) models with bias, variance, and confusion matrices"],"prefix":"10.1371","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-3206-4048","authenticated-orcid":true,"given":"Christopher","family":"Wang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Elianna","family":"Schimke","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tristan","family":"Kako","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Aiden","family":"Gao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Martina","family":"Lamberti","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Joost","family":"le Feber","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5386-1101","authenticated-orcid":true,"given":"Sarah","family":"Marzen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"340","published-online":{"date-parts":[[2026,8,11]]},"reference":[{"key":"pone.0342165.ref001","first-page":"25","article-title":"Prediction, cognition and the brain","volume":"4","author":"A Bubic","year":"2010","journal-title":"Front Hum Neurosci"},{"issue":"2","key":"pone.0342165.ref002","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1016\/j.neuron.2015.06.033","article-title":"How Can Single Sensory Neurons Predict Behavior?","volume":"87","author":"X Pitkow","year":"2015","journal-title":"Neuron"},{"key":"pone.0342165.ref003","volume-title":"Elements of information theory","author":"TM, Thomas JA Cover","year":"1999"},{"issue":"1","key":"pone.0342165.ref004","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1103\/PhysRevLett.80.197","article-title":"Entropy and Information in Neural Spike Trains","volume":"80","author":"SP Strong","year":"1998","journal-title":"Phys Rev Lett"},{"issue":"9","key":"pone.0342165.ref005","doi-asserted-by":"crossref","first-page":"3354","DOI":"10.1073\/pnas.1309933111","article-title":"Equitability, mutual information, and the maximal information coefficient","volume":"111","author":"JB Kinney","year":"2014","journal-title":"Proc Natl Acad Sci U S A"},{"issue":"6","key":"pone.0342165.ref006","doi-asserted-by":"crossref","first-page":"1191","DOI":"10.1162\/089976603321780272","article-title":"Estimation of Entropy and Mutual Information","volume":"15","author":"L Paninski","year":"2003","journal-title":"Neural Computat"},{"key":"pone.0342165.ref007","article-title":"Entropy and inference, revisited","volume":"14","author":"I Nemenman","year":"2001","journal-title":"Adv Neural Inform Process Syst"},{"key":"pone.0342165.ref008","first-page":"2833","article-title":"Bayesian entropy estimation for countable discrete distributions","volume":"15","author":"E Archer","year":"2014","journal-title":"J Mach Learn Res"},{"key":"pone.0342165.ref009","unstructured":"Poole B, Ozair S, Van Den Oord A, Alemi A, Tucker G. 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