A Unified Interface for Covariance and Precision Geostatistical Inference

A Unified Interface for Covariance and Precision Geostatistical Inference | 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 A Unified Interface for Covariance and Precision Geostatistical Inference Juan Jose Segura This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8805990/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 A common geostatistical pipeline can be implemented either with a dense covariance action or with a sparse precision action, depending on whether the prior is specified by a kernel or by a stochastic PDE or graph Laplacian. In practice, switching between these backends often forces one to re-derive formulas and re-implement inference. We present a unified, compositional interface for linear Gaussian geostatistical models that separates (i) where the latent field is represented, (ii) how measurements and targets are assembled from linear operators, and (iii) how inference is performed. The same assembled model can be executed by two interchangeable backends: a covariance-first method that solves in measurement space and a precision-first method that solves in latent space. We show that both compute the same posterior mean and expose the same matrix-free posterior covariance operator, enabling uncertainty quantification without forming dense matrices. We give practical algorithms for marginal variance estimation via Hutchinson trace estimators and for conditional simulation via Lanczos methods. Intrinsic, rankdeficient precisions are handled compositionally using projector constraints and projected preconditioned conjugate gradients. A complexity comparison clarifies the regimes in which each backend is preferable. Mathematics Subject Classification (2020) 18B40 · 62M30 · 65F10 · 62F15 geostatistics Gaussian processes Gaussian Markov random fields Markov categories dagger categories matrix-free inference 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. 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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-8805990","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":616795083,"identity":"20459bc5-9fde-48b5-a330-18c7ac1d4686","order_by":0,"name":"Juan Jose Segura","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA8ElEQVRIiWNgGAWjYBACxgZkXkUFkJAA4gdEazlzBqolgWg7z7YRoYV5RvKzBwx/bOw23D78gOHgvMN5/LMbGD/g08I4I83cgLEtLXnDuTQDhoPbDhdL3DnALIFfS4KZBGPD4WSDMwwGzB+3HU5suJHAhtdhjDPSv0kw/PkP1ML+geHgnMOJ8wlryTGTYGA7YGdwhgfosIbDiRsIaul5UyaR2JacIHmGp+DAgWPpiRvvHGzG6xfD9vRtEh/+2NnznWHf+OBAjXXivNvNBz98wKelgQEcC4kg+gDU5gY8GhgY5KG0PV5Vo2AUjIJRMLIBAD+qVXs9wZiVAAAAAElFTkSuQmCC","orcid":"","institution":"Andrés Bello National University","correspondingAuthor":true,"prefix":"","firstName":"Juan","middleName":"Jose","lastName":"Segura","suffix":""}],"badges":[],"createdAt":"2026-02-06 10:53:29","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8805990/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8805990/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":106080652,"identity":"aa23868f-c335-4afa-afa0-32e98f2ca641","added_by":"auto","created_at":"2026-04-03 08:30:40","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":257838,"visible":true,"origin":"","legend":"","description":"","filename":"geogpacssubmission.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8805990/v1_covered_1d47661b-cbf0-462c-aaeb-020aedce0d3c.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A Unified Interface for Covariance and Precision Geostatistical Inference","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":"geostatistics, Gaussian processes, Gaussian Markov random fields, Markov categories, dagger categories, matrix-free inference","lastPublishedDoi":"10.21203/rs.3.rs-8805990/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8805990/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eA common geostatistical pipeline can be implemented either with a dense covariance action or with a sparse precision action, depending on whether the prior is specified by a kernel or by a stochastic PDE or graph Laplacian. 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