LoCal-SBI: Localized Summary Learning and Mondrian Posterior Calibration for Reliable Simulation-Based Inference

LoCal-SBI: Localized Summary Learning and Mondrian Posterior Calibration for Reliable Simulation-Based 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 LoCal-SBI: Localized Summary Learning and Mondrian Posterior Calibration for Reliable Simulation-Based Inference Yutong Zhang, Yaoran Yang, Yifan Zhu, Wentao Zhang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9360238/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 6 You are reading this latest preprint version Abstract Simulation-based inference (SBI) provides a principled route to parameter inference when a simulator is available but pointwise likelihood evaluation is infeasible. Two technical bottlenecks nevertheless remain central in practical statistical computing: learning low-dimensional summaries that are informative for the \emph{particular} observed dataset, and delivering uncertainty regions that remain reliable after approximate inference. Existing work has substantially advanced these directions, but largely in parallel rather than jointly. This paper introduces \emph{LoCal-SBI}, a unified procedure that couples observed-data-specific summary refinement with stratified conformal calibration of posterior regions. The method first learns a pilot global map on prior-predictive simulations. For a given observation, it then localizes simulations in the pilot posterior space and refits a weighted summary map in that neighborhood. An empirical Gibbs posterior is formed over the simulated particles, and ellipsoidal credible regions are subsequently calibrated by Mondrian conformal quantiles computed within pilot-defined strata. The resulting procedure admits a transparent statistical analysis: we establish a local bias--variance bound for the learned summary map, a posterior perturbation inequality transferring summary error to posterior mean error, a finite-sample cell-conditional coverage guarantee for the calibrated regions, and a weak-misspecification bound showing that nuisance shifts enter only through the local nuisance sensitivity of the summary operator. Experiments on a curved banana benchmark, the g-and-k model, and a regime-switching nuisance-shift benchmark show that localization and calibration are complementary: localization improves posterior geometry and point accuracy, whereas conformalization restores reliability without the excessive conservatism of global baselines. Across the reported benchmarks, LoCal-SBI consistently improves posterior mean accuracy relative to globally calibrated summary baselines while producing materially smaller calibrated credible regions. simulation-based inference approximate Bayesian computation conformal calibration summary statistics uncertainty quantification misspecification Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 08 May, 2026 Reviewers agreed at journal 13 Apr, 2026 Reviewers invited by journal 13 Apr, 2026 Editor assigned by journal 11 Apr, 2026 Submission checks completed at journal 10 Apr, 2026 First submitted to journal 08 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. 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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-9360238","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":622477005,"identity":"eeef211e-2df7-4090-a0d1-baa7d05a3700","order_by":0,"name":"Yutong Zhang","email":"","orcid":"","institution":"Sichuan University","correspondingAuthor":false,"prefix":"","firstName":"Yutong","middleName":"","lastName":"Zhang","suffix":""},{"id":622477006,"identity":"633dd310-7a2b-4938-8d43-ea21b23443c3","order_by":1,"name":"Yaoran Yang","email":"","orcid":"","institution":"Sichuan University","correspondingAuthor":false,"prefix":"","firstName":"Yaoran","middleName":"","lastName":"Yang","suffix":""},{"id":622477007,"identity":"a44dbf85-ec6d-485b-a660-a34dda66d871","order_by":2,"name":"Yifan Zhu","email":"","orcid":"","institution":"Sichuan University","correspondingAuthor":false,"prefix":"","firstName":"Yifan","middleName":"","lastName":"Zhu","suffix":""},{"id":622477008,"identity":"33162166-ea3d-4e77-bf0d-ca0d30b6281c","order_by":3,"name":"Wentao Zhang","email":"data:image/png;base64,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","orcid":"","institution":"Tsinghua University","correspondingAuthor":true,"prefix":"","firstName":"Wentao","middleName":"","lastName":"Zhang","suffix":""}],"badges":[],"createdAt":"2026-04-08 18:23:25","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9360238/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9360238/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":107485168,"identity":"e0477d42-833f-4db1-811f-a32a10abc894","added_by":"auto","created_at":"2026-04-22 02:33:46","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":641881,"visible":true,"origin":"","legend":"","description":"","filename":"SBI.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9360238/v1_covered_838f6b85-6c91-42c7-9ae1-c68f20d8ca0c.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"LoCal-SBI: Localized Summary Learning and Mondrian Posterior Calibration for Reliable Simulation-Based Inference","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":"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":"simulation-based inference, approximate Bayesian computation, conformal calibration, summary statistics, uncertainty quantification, misspecification","lastPublishedDoi":"10.21203/rs.3.rs-9360238/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9360238/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Simulation-based inference (SBI) provides a principled route to parameter inference when a simulator is available but pointwise likelihood evaluation is infeasible. 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