Efficient Modeling of Quasi-Periodic Data with Seasonal Gaussian Process

Efficient Modeling of Quasi-Periodic Data with Seasonal Gaussian Process | 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 Efficient Modeling of Quasi-Periodic Data with Seasonal Gaussian Process Ziang Zhang, Patrick Brown, Jamie Stafford This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3359335/v2 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 18 Jan, 2025 Read the published version in Statistics and Computing → Version 2 posted 8 You are reading this latest preprint version Show more versions Abstract Quasi-periodicity refers to a pattern in a function where it appears periodic at a certain frequency but exhibits evolving amplitudes over time. This is often the case in practical settings such as the modeling of case counts of infectious disease or the population dynamics of species over time.In this paper, we consider a class of Gaussian processes, called seasonal Gaussian Processes (sGP), for model-based inference of such quasi-periodic behavior. We illustrate that the exact sGP can be efficiently fitted using its state space representation for equally spaced time points.However, for large datasets with irregular spacing, the exact approach becomes computationally inefficient and unstable. To address this, we develop a continuous finite dimensional approximation for sGP using the seasonal B-spline (sB-spline) basis constructed by damping B-splines with sinusoidal functions. We prove the covariance convergence rate of the proposed approximation to the true sGP as the number of basis functions increases, and show its superior approximation quality through numerical studies.We also provide a unified and interpretable way to define priors for the sGP, based on the notion of predictive standard deviation (PSD).Finally, we implement the proposed inference method on several real data examples to illustrate its practical usage. Full Text Additional Declarations No competing interests reported. Supplementary Files supplement.pdf Cite Share Download PDF Status: Published Journal Publication published 18 Jan, 2025 Read the published version in Statistics and Computing → Version 2 posted Editorial decision: Accepted 06 Jan, 2025 Reviews received at journal 23 Dec, 2024 Reviews received at journal 06 Dec, 2024 Reviewers agreed at journal 02 Dec, 2024 Reviewers agreed at journal 02 Dec, 2024 Reviewers invited by journal 02 Dec, 2024 Submission checks completed at journal 27 Nov, 2024 First submitted to journal 27 Nov, 2024 You are reading this latest preprint version Show more versions 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. 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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-3359335","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[{"code":1,"date":"2023-09-26 13:29:08","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research 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