Sequential Adaptive Priors for Orthogonal Functions *

Sequential Adaptive Priors for Orthogonal Functions * | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Sequential Adaptive Priors for Orthogonal Functions * Shonosuke Sugasawa, Daichi Mochihashi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8641060/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract We propose a novel class of prior distributions for sequences of orthogonal functions , which are frequently required in various statistical models such as functional principal component analysis (FPCA). Our approach constructs priors sequentially by imposing adaptive orthogonality constraints through a hierarchical formulation of conditionally normal distributions. The orthogonality is controlled via hyperparameters, allowing for flexible trade-offs between exactness and smoothness, which can be learned from the observed data. We illustrate the properties of the proposed prior and show that it leads to nearly orthogonal posterior estimates. The proposed prior is employed in Bayesian FPCA, providing more interpretable principal functions and efficient low-rank representations. Through simulation studies and analysis of human mobility data in Tokyo, we demonstrate the superior performance of our approach in inducing orthogonality and improving functional component estimation. Basis function expansion Functional principal component analysis Gibbs sampler Markov Chain Monte Carlo Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8641060","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":581897859,"identity":"7fe3e74d-a1be-44b8-8469-059d4da0635f","order_by":0,"name":"Shonosuke Sugasawa","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABA0lEQVRIiWNgGAWjYDADfgiVwMAGYbAR1iLZQLIWgwNQLQSB/Iz0ix9/1ByWNz7e/PBxAUOaHB97A+OHHwx8eTgNv5FTLM1z7LDhtjPHjI1nMOQYs/EcYJbsYWArxqlFIidBmoHtNuO2Gzls0jwMFYltEgkM0kC/JDbgdFhO8s8f/27bb57/BqylHqiF+Tc+LQw30o9J8LbdTtwgwQPSkpPAJpHAhtcWgzNv2Kx5+/4nzziTZmzMY5Bm2MZzsM2yxwC3X+Tb0x/f/PEtzba//fDDxzwVyfLy7c2Hb/yoOIYzxBgYeAyQLQURjEAnGRxLwK2F/QFW4Ro8WkbBKBgFo2CEAQDR2VDV2TAMPwAAAABJRU5ErkJggg==","orcid":"","institution":"Keio University","correspondingAuthor":true,"prefix":"","firstName":"Shonosuke","middleName":"","lastName":"Sugasawa","suffix":""},{"id":581897860,"identity":"3ae111c1-f2de-45bc-b52b-68c5e3e429ba","order_by":1,"name":"Daichi Mochihashi","email":"","orcid":"","institution":"The Institute of Statistical Mathematics","correspondingAuthor":false,"prefix":"","firstName":"Daichi","middleName":"","lastName":"Mochihashi","suffix":""}],"badges":[],"createdAt":"2026-01-19 15:42:57","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8641060/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8641060/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":107483526,"identity":"8c8636bc-b1f0-4f51-a36c-3fe6ec0472ce","added_by":"auto","created_at":"2026-04-22 02:28:05","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":401103,"visible":true,"origin":"","legend":"","description":"","filename":"source.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8641060/v1_covered_8e00038a-57fc-4910-91a3-51e7e4c31122.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Sequential Adaptive Priors for Orthogonal Functions *","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Basis function expansion, Functional principal component analysis, Gibbs sampler, Markov Chain Monte Carlo","lastPublishedDoi":"10.21203/rs.3.rs-8641060/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8641060/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"We propose a novel class of prior distributions for sequences of orthogonal functions , which are frequently required in various statistical models such as functional principal component analysis (FPCA). 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