A Generalized Unified Skew-Normal Process with Neural Bayes Inference

A Generalized Unified Skew-Normal Process with Neural Bayes 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 Generalized Unified Skew-Normal Process with Neural Bayes Inference Kesen Wang, Marc Genton This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7296705/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 18 Jan, 2026 Read the published version in Statistics and Computing → Version 1 posted 9 You are reading this latest preprint version Abstract In recent decades, statisticians have been increasingly { encountering} spatial data that exhibit non-Gaussian behaviors such as asymmetry and heavy-tailedness. As a result, the assumptions of symmetry and fixed tail weight in Gaussian processes have become restrictive and may fail to capture the intrinsic properties of the data. To address the limitations of the Gaussian models, a variety of skewed models has been proposed, of which the popularity has grown rapidly. These skewed models introduce parameters that govern skewness and tail weight. Among various proposals in the literature, unified skewed distributions, such as the Unified Skew-Normal (SUN), have received considerable attention. In this work, we revisit a more concise and intepretable re-parameterization of the SUN distribution and apply the distribution to random fields by constructing a generalized unified skew-normal (GSUN) spatial process. We demonstrate { that the GSUN is a valid spatial process by showing its vanishing correlation at large distances} and provide the corresponding spatial interpolation method. In addition, we develop an inference mechanism for the GSUN process using the concept of neural Bayes estimators with deep graphical attention networks (GATs) and encoder transformer. We show the superiority of our proposed estimator over the conventional CNN-based architectures regarding stability and accuracy by means of a simulation study. In addition, we demonstrate that the GSUN process offers enhanced flexibility compared to another model proposed in the literature through an application to Pb-contaminated soil data. Furthermore, we show that the GSUN process is different from the conventional Gaussian processes and Tukey g -and- h processes, through the probability integral transform (PIT). Encoder transformer Graphical attention network Neural Bayes estimator Non-Gaussian process Unified skew-normal distribution Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 18 Jan, 2026 Read the published version in Statistics and Computing → Version 1 posted Editorial decision: Revision requested 06 Oct, 2025 Reviews received at journal 06 Oct, 2025 Reviews received at journal 19 Sep, 2025 Reviewers agreed at journal 02 Sep, 2025 Reviewers agreed at journal 01 Sep, 2025 Reviewers invited by journal 29 Aug, 2025 Editor assigned by journal 05 Aug, 2025 Submission checks completed at journal 05 Aug, 2025 First submitted to journal 05 Aug, 2025 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-7296705","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":509455063,"identity":"eb1ca131-c8d1-4927-9e87-8646e0258aed","order_by":0,"name":"Kesen Wang","email":"data:image/png;base64,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","orcid":"","institution":"King Abdullah University of Science and Technology","correspondingAuthor":true,"prefix":"","firstName":"Kesen","middleName":"","lastName":"Wang","suffix":""},{"id":509455064,"identity":"8c2a4531-6dee-4f77-845f-6567f88ec631","order_by":1,"name":"Marc Genton","email":"","orcid":"","institution":"King Abdullah University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Marc","middleName":"","lastName":"Genton","suffix":""}],"badges":[],"createdAt":"2025-08-05 05:53:22","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7296705/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7296705/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s11222-025-10801-9","type":"published","date":"2026-01-18T16:29:01+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":100616048,"identity":"a35995cc-76d7-41c9-8238-3e02d5c7af23","added_by":"auto","created_at":"2026-01-19 17:38:46","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":953684,"visible":true,"origin":"","legend":"","description":"","filename":"2024GSUN.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7296705/v1_covered_536b8614-ed4f-455a-ba08-200d88ffb7f0.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A Generalized Unified Skew-Normal Process with Neural Bayes Inference","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"statistics-and-computing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"stco","sideBox":"Learn more about [Statistics and Computing](http://link.springer.com/journal/11222)","snPcode":"11222","submissionUrl":"https://submission.nature.com/new-submission/11222/3","title":"Statistics and Computing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Encoder transformer, Graphical attention network, Neural Bayes estimator, Non-Gaussian process, Unified skew-normal distribution","lastPublishedDoi":"10.21203/rs.3.rs-7296705/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7296705/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn recent decades, statisticians have been increasingly { encountering} spatial data that exhibit non-Gaussian behaviors such as asymmetry and heavy-tailedness. \u0026nbsp;As a result, the assumptions of symmetry and fixed tail weight in Gaussian processes have become restrictive and may fail to capture the intrinsic properties of the data. 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