Nested and Additive Skew-Gaussian Tukey-$h$ Processes for Environmental Extremes

Nested and Additive Skew-Gaussian Tukey-$h$ Processes for Environmental Extremes | 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 Nested and Additive Skew-Gaussian Tukey-$h$ Processes for Environmental Extremes Negar Alizadeh, Majid Jafari Khaledi, Hamid Zareifard This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9385614/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 4 You are reading this latest preprint version Abstract Spatial data arising in environmental and ecological studies often exhibit marked skewness and heavy-tailed behavior, posing challenges for conventional Gaussian spatial random effects models. To address these limitations, we develop a class of skew-Gaussian Tukey-$h$ (SGTH) spatial processes that provide flexible control over both skewness and tail heaviness. We introduce two constructions of SGTH spatial fields, referred to as the nested and additive formulations, which induce non-Gaussian behavior through distinct structural mechanisms. We investigate key marginal and dependence properties of the proposed processes and embed them within a Bayesian hierarchical framework for modeling spatially indexed data using SGTH random effects. Posterior inference is conducted via Markov chain Monte Carlo methods, using a data augmentation strategy and scalable local updates to handle the non-Gaussian latent structure. Through simulation studies, we explore the inferential behavior of the two constructions and illustrate their practical implications. The proposed methodology is further demonstrated through the analysis of a georeferenced rainfall dataset. Geostatistics Skew-normal tukey-h distribution Heavy tails Skewness Bayesian hierarchical models Spatial Random effects Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 16 Apr, 2026 Editor assigned by journal 16 Apr, 2026 Submission checks completed at journal 15 Apr, 2026 First submitted to journal 11 Apr, 2026 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-9385614","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":624312970,"identity":"469b221f-9761-48ba-ac52-dfbad5515761","order_by":0,"name":"Negar Alizadeh","email":"","orcid":"","institution":"Tarbiat Modares University","correspondingAuthor":false,"prefix":"","firstName":"Negar","middleName":"","lastName":"Alizadeh","suffix":""},{"id":624312971,"identity":"57de532c-d451-4023-9fc1-63e1baaa7a32","order_by":1,"name":"Majid Jafari Khaledi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA50lEQVRIiWNgGAWjYBACxgbGBwwJDAxyQLYBXPQAfi3MBiAtxsRrYWBgBqtMbEDWgl9D+2G2Dw8YtqWvbW/e+Lmioo6Bv/0A4+EKfA7rSWaekcBwO3fbmWPFkmfOHGaQOJPAcPAMXr/kH2ZI/AfUciPHQLKxDeiLGwwMBxvwael/zAz0/u10sxs5xj8b/9UxyBPUMiMZrCUBqMVMsrGBmcGAsBaILYZAv5RZNhw7zGN4JrEBrxbD/mRmxh8Mt+XNjjdvvtlQUycnd/zw4Y94taBL8oCCBI8GBgZ5vLKjYBSMglEwCkAAAL7XUUZ5dB2QAAAAAElFTkSuQmCC","orcid":"","institution":"Tarbiat Modares University","correspondingAuthor":true,"prefix":"","firstName":"Majid","middleName":"Jafari","lastName":"Khaledi","suffix":""},{"id":624312972,"identity":"f0ea3d78-4117-44c4-8991-9f878b90aed9","order_by":2,"name":"Hamid Zareifard","email":"","orcid":"","institution":"Jahrom University","correspondingAuthor":false,"prefix":"","firstName":"Hamid","middleName":"","lastName":"Zareifard","suffix":""}],"badges":[],"createdAt":"2026-04-11 07:38:29","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9385614/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9385614/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":108771482,"identity":"6e21839d-431d-4db4-9113-ce5a7ec7136b","added_by":"auto","created_at":"2026-05-08 08:30:29","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3301292,"visible":true,"origin":"","legend":"","description":"","filename":"SRFnew2.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9385614/v1_covered_d182d87c-6b5d-434f-a586-b27621c58f21.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Nested and Additive Skew-Gaussian Tukey-$h$ Processes for Environmental Extremes","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"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":"stochastic-environmental-research-and-risk-assessment","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"serr","sideBox":"Learn more about [Stochastic Environmental Research and Risk Assessment](https://www.springer.com/journal/477)","snPcode":"477","submissionUrl":"https://submission.nature.com/new-submission/477/3","title":"Stochastic Environmental Research and Risk Assessment","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Geostatistics, Skew-normal tukey-h distribution, Heavy tails, Skewness, Bayesian hierarchical models, Spatial Random effects","lastPublishedDoi":"10.21203/rs.3.rs-9385614/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9385614/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":" \nSpatial data arising in environmental and ecological studies often exhibit marked skewness and heavy-tailed behavior, posing challenges for conventional Gaussian spatial random effects models. To address these limitations, we develop a class of skew-Gaussian Tukey-$h$ (SGTH) spatial processes that provide flexible control over both skewness and tail heaviness. We introduce two constructions of SGTH spatial fields, referred to as the nested and additive formulations, which induce non-Gaussian behavior through distinct structural mechanisms. We investigate key marginal and dependence properties of the proposed processes and embed them within a Bayesian hierarchical framework for modeling spatially indexed data using SGTH random effects. \nPosterior inference is conducted via Markov chain Monte Carlo methods, \nusing a data augmentation strategy and scalable local updates to handle the non-Gaussian latent structure.\nThrough simulation studies, we explore the inferential behavior of the two constructions and illustrate their practical implications. 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