Variational Bayes Inference for Spatio-temporal Dynamic Factor Models

Variational Bayes Inference for Spatio-temporal Dynamic Factor Models | 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 Variational Bayes Inference for Spatio-temporal Dynamic Factor Models Guilherme Colombo Soares, Marcio Poletti Laurini This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7734705/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 investigate fast variational approximations for spatio–temporal dynamic factor models, benchmarking them against a Markov Chain Monte Carlo (MCMC) baseline. We propose two Coordinate Ascent Variational Inference (CAVI) schemes: (i) a mean-field variational Bayes (MFVB) that factorizes states and spatial loadings, and (ii) a structured variational Bayes (SVB) that preserves autoregressive state dependence while maintaining a mean-field structure across space. Using monthly NCEP/NCAR 1000 mb air temperature data over North America (1948–2025; 928 months; 204 locations), we find that SVB closely reproduces the MCMC posterior in both latent states and spatial loadings, whereas MFVB diverges more from the posterior but often achieves the strongest out-of-sample forecasts across 1–12 month horizons. In terms of computation, MFVB and SVB are approximately 246 times and 60 times faster than MCMC, respectively. These results underscore a practical trade-off: SVB prioritizes posterior fidelity, while MFVB maximizes speed and forecasting performance. Markov Chain Monte Carlo Variational Bayes Coordinate Ascent Variational Inference Mean-field approximation Spatio-temporal dynamic factor models 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-7734705","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":522529962,"identity":"fbf37f1d-e446-47bc-9e2c-552490a70314","order_by":0,"name":"Guilherme Colombo Soares","email":"","orcid":"https://orcid.org/0009-0001-6635-7534","institution":"Universidade de São Paulo","correspondingAuthor":false,"prefix":"","firstName":"Guilherme","middleName":"Colombo","lastName":"Soares","suffix":""},{"id":522529963,"identity":"3d4e969e-8d28-4542-9b08-a735903ac203","order_by":1,"name":"Marcio Poletti Laurini","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA2UlEQVRIiWNgGAWjYBACPhCRwCAhx94AF+PBr4UNqsWY5wBJWoAgsYd4LexnzD483GGR3sPe/OxzAcNhe3MG3mMf8GrhyTGekXhGIreH55jx7BkMhxN3NvAlz8DvsBxjhsQ2idz9EgnGzDwMhxMMDvAY43cY/xuwlnQe+eefQVrsCWuRgNiSwCPBA7aFcQNhLc+KQVoMe3hyiplnGKQn7mzmS8arhZ8/eTPjz7Y6eR7245uZCyqs7c3Zew/j1YICmBkMGBgMmInXANICBAak6BgFo2AUjIIRAQAJqTm7s3kmRQAAAABJRU5ErkJggg==","orcid":"","institution":"Universidade de São Paulo","correspondingAuthor":true,"prefix":"","firstName":"Marcio","middleName":"Poletti","lastName":"Laurini","suffix":""}],"badges":[],"createdAt":"2025-09-28 13:38:14","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7734705/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7734705/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":92995613,"identity":"bf8d2a78-2a66-4267-ac07-0ad73d4fa2c0","added_by":"auto","created_at":"2025-10-08 03:15:52","extension":"json","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":3785,"visible":true,"origin":"","legend":"","description":"","filename":"07b91a2de4ce43a4a64459124875fb20.json","url":"https://assets-eu.researchsquare.com/files/rs-7734705/v1/1ea8253675c81781baf5a788.json"},{"id":97250742,"identity":"31a6d305-e06e-45fe-ba8f-fa58789c3b97","added_by":"auto","created_at":"2025-12-02 13:15:08","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":929213,"visible":true,"origin":"","legend":"","description":"","filename":"sub.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7734705/v1_covered_b451a5f1-4b5f-4110-a630-b50486b7341c.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Variational Bayes Inference for Spatio-temporal Dynamic Factor Models","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"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":"Markov Chain Monte Carlo, Variational Bayes, Coordinate Ascent Variational Inference, Mean-field approximation, Spatio-temporal dynamic factor models","lastPublishedDoi":"10.21203/rs.3.rs-7734705/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7734705/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"We investigate fast variational approximations for spatio–temporal dynamic factor models, benchmarking them against a Markov Chain Monte Carlo (MCMC) baseline. 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