{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:23:22Z","timestamp":1760243002178,"version":"build-2065373602"},"reference-count":12,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2015,4,23]],"date-time":"2015-04-23T00:00:00Z","timestamp":1429747200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Nucleo de Apoio a Pesquisa CNAIPS USP"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>A systematic method of transferring information from coarser to finer resolution based on renormalization group (RG) transformations is introduced. It permits building informative priors in finer scales from posteriors in coarser scales since, under some conditions, RG transformations in the space of hyperparameters can be inverted. These priors are updated using renormalized data into posteriors by Maximum Entropy. The resulting inference method, backward RG (BRG) priors, is tested by doing simulations of a functional magnetic resonance imaging (fMRI) experiment. Its results are compared with a Bayesian approach working in the finest available resolution. Using BRG priors sources can be partially identified even when signal to noise ratio levels are up to ~ -25dB improving vastly on the single step Bayesian approach. For low levels of noise the BRG prior is not an improvement over the single scale Bayesian method. Analysis of the histograms of hyperparameters can show how to distinguish if the method is failing, due to very high levels of noise, or if the identification of the sources is, at least partially possible.<\/jats:p>","DOI":"10.3390\/e17052573","type":"journal-article","created":{"date-parts":[[2015,4,23]],"date-time":"2015-04-23T11:40:29Z","timestamp":1429789229000},"page":"2573-2589","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Source Localization by Entropic Inference and Backward Renormalization Group Priors"],"prefix":"10.3390","volume":"17","author":[{"given":"Nestor","family":"Caticha","sequence":"first","affiliation":[{"name":"Departamento de F\u00edsica Geral, Instituto de F\u00edsica, Universidade de S\u00e3o Paulo, CP 66318, 05315-970, S\u00e3o Paulo-SP, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,4,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1103\/RevModPhys.55.583","article-title":"The Renormalization Group and Critical Phenomena","volume":"55","author":"Wilson","year":"1983","journal-title":"Rev. Mod. Phys"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2035","DOI":"10.1103\/PhysRevD.40.2035","article-title":"Multigrid Monte Carlo Method. Conceptual Foundations","volume":"40","author":"Goodman","year":"1989","journal-title":"Phys. Rev. D"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"654","DOI":"10.1016\/j.neuroimage.2004.06.011","article-title":"Multigrid Priors for a Bayesian Approach to FMRI","volume":"23","author":"Amaral","year":"2004","journal-title":"NeuroImage"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Giffin, A., and Caticha, A. (2007, January 8\u201313). Updating Probabilities with Data and Moments. Saratoga Springs, NY, USA.","DOI":"10.1063\/1.2821302"},{"key":"ref_5","unstructured":"Bishop, C.M. (2007). Pattern Recognition and Machine Learning, Springer. 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Bayes and Empirical Bayes methods for Data Analysis, Chapman and Hall\/CRC."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/5\/2573\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:45:12Z","timestamp":1760215512000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/5\/2573"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,4,23]]},"references-count":12,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2015,5]]}},"alternative-id":["e17052573"],"URL":"https:\/\/doi.org\/10.3390\/e17052573","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2015,4,23]]}}}