Combining Adaptive MCMC and Nested Sampling for Robust Bayesian Model Selection with reduced prior sensitivity

Combining Adaptive MCMC and Nested Sampling for Robust Bayesian Model Selection with reduced prior sensitivity | 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 Combining Adaptive MCMC and Nested Sampling for Robust Bayesian Model Selection with reduced prior sensitivity José Carlos García-Merino, Miracle Amadi, Enrique García-Macías, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6838854/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 13 Feb, 2026 Read the published version in Statistics and Computing → Version 1 posted 9 You are reading this latest preprint version Abstract Bayes Factors provide a rigorous methodology for the Bayesian assessment of competing models. However, this approach faces inherent challenges. The computation of Bayesian evidence often involves evaluating high-dimensional, analytically intractable integrals. Moreover, Bayesian evidence is particularly sensitive to prior assumptions, which can significantly bias model comparison. While extensive research has been conducted to address the former limitation, the latter remains a challenging open area of research. To address this issue, this work introduces DRAM-NS, a new methodology combining Nested Sampling (NS) with adaptive Markov Chain Monte Carlo (MCMC) techniques for Bayesian model selection. Specifically, the developed technique enhances the traditional NS algorithm by incorporating a preliminary MCMC step on a subset of the available data, allowing for natural integration of non-informative or improper priors. The effectiveness of the proposed approach is demonstrated through several case studies. Numerical results and discussion demonstrate that DRAM-NS provides a more reliable framework than standard NS alone for model selection in scenarios where prior knowledge is uncertain. Bayesian evidence Markov Chain Monte Carlo Model selection Nested Sampling Prior sensitivity Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 13 Feb, 2026 Read the published version in Statistics and Computing → Version 1 posted Editorial decision: Revision requested 12 Sep, 2025 Reviews received at journal 10 Sep, 2025 Reviews received at journal 11 Jul, 2025 Reviewers agreed at journal 03 Jul, 2025 Reviewers agreed at journal 02 Jul, 2025 Reviewers invited by journal 01 Jul, 2025 Editor assigned by journal 08 Jun, 2025 Submission checks completed at journal 07 Jun, 2025 First submitted to journal 06 Jun, 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-6838854","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":479464790,"identity":"2708162b-dc05-475c-a196-6e681c49d7ea","order_by":0,"name":"José Carlos García-Merino","email":"","orcid":"","institution":"National University of Distance Education","correspondingAuthor":false,"prefix":"","firstName":"José","middleName":"Carlos","lastName":"García-Merino","suffix":""},{"id":479464791,"identity":"ef3f61e0-41a1-48cd-90d1-5aae8decc66b","order_by":1,"name":"Miracle Amadi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA1UlEQVRIiWNgGAWjYDACZhBRAGFLJFRYACnGBwcIazGAaTkjwcDDwGyAXwsDshbGNogWvIp123kffvhhYMPAP+3wwxsP50kk7mdgZsRri9lhdmPJHoM0BonbacYWidskEnuAbiWghY1BmsHgMAPD7QQzCYgW/gOEtDD/ZjD4zyB/O/2bROIc4mxhA9pygMHgdg7QlgYitVj2GCTzGN7OKbZIOCZh3HOYkJbzx5hv/Kiwk5O7nb7x5o8aG9n29mbmD/i0wAAPgslMjPpRMApGwSgYBXgBAJFDQn6USV1kAAAAAElFTkSuQmCC","orcid":"","institution":"Lappeenranta University of Technology","correspondingAuthor":true,"prefix":"","firstName":"Miracle","middleName":"","lastName":"Amadi","suffix":""},{"id":479464792,"identity":"d45f8e80-ea3c-4f1a-9de5-476876c082ba","order_by":2,"name":"Enrique García-Macías","email":"","orcid":"","institution":"University of Granada","correspondingAuthor":false,"prefix":"","firstName":"Enrique","middleName":"","lastName":"García-Macías","suffix":""},{"id":479464793,"identity":"70e4bb53-e70f-4e27-8286-856611df31cc","order_by":3,"name":"Carmen Calvo-Jurado","email":"","orcid":"","institution":"University of Extremadura","correspondingAuthor":false,"prefix":"","firstName":"Carmen","middleName":"","lastName":"Calvo-Jurado","suffix":""},{"id":479464795,"identity":"453509d2-5668-46b2-87bd-12a1ab4fa33e","order_by":4,"name":"Heikki Haario","email":"","orcid":"","institution":"Lappeenranta University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Heikki","middleName":"","lastName":"Haario","suffix":""}],"badges":[],"createdAt":"2025-06-06 17:38:13","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6838854/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6838854/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s11222-026-10843-7","type":"published","date":"2026-02-13T15:57:15+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":102786224,"identity":"71a1caed-9bc7-429a-8cb6-e3b5a21dd1e8","added_by":"auto","created_at":"2026-02-16 16:12:21","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":369039,"visible":true,"origin":"","legend":"","description":"","filename":"SUBMISSIONSTATSCOMP.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6838854/v1_covered_5ca8a7ed-f29c-44a2-8164-c981846328e8.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Combining Adaptive MCMC and Nested Sampling for Robust Bayesian Model Selection with reduced prior sensitivity","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":"Bayesian evidence, Markov Chain Monte Carlo, Model selection, Nested Sampling, Prior sensitivity","lastPublishedDoi":"10.21203/rs.3.rs-6838854/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6838854/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eBayes Factors provide a rigorous methodology for the Bayesian assessment of competing models. 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