On Bayesian inference in pulsar timing arrays: identifiability and choice of the priors

On Bayesian inference in pulsar timing arrays: identifiability and choice of the priors | 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 On Bayesian inference in pulsar timing arrays: identifiability and choice of the priors Luca Martino, Francesco Alì, Aldo Barca, Fatima Modica Bittordo, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8351930/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 Pulsar Timing Arrays (PTAs) represent one of the most active and rapidly evolving research areas in contemporary astrophysics.PTAs use pulsar observations to search for gravitational waves, relying on accurate statistical models of pulsar timing data. In this work, we revisit the bias problem reported in both Bayesian and frequentist analyses and identify the structural features of the statistical models that give rise to these effects. We show that it originates from an underlying identifiability issue in commonly used linear Gaussian models. We outline and discuss different possible remedies to the non-identifiability. For instance, one possible approach is the use of hierarchical priors, which can alleviate non-identifiability but at the cost of making the inference strongly prior-dependent: the choice of the prior effectively selects one specific set of parameters among infinitely many equivalent solutions. Hence, in these non-identifiable models, the resulting inference outputs along the non-identifiable directions are effectively determined by the choice of the prior, rather than by the data themselves (becoming completely prior-driven).Moreover, we also highlight the limitations of the use of diffuse and improper priors in Bayesian model selection, as they can distort Bayes factors and compromise the robustness of gravitational-wave detection analyses.Finally, we give an overview of best practice for prior choice in model selection and suggest possible remedies to the limitations of linear PTA models reported in literature. Pulsar timing arrays (PTAs) Bayesian inference Linear Gaussian models identifiability Prior densities 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. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-8351930","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":604027664,"identity":"0919835b-1803-4517-8e5b-edc52dae59bb","order_by":0,"name":"Luca Martino","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA10lEQVRIiWNgGAWjYBACPjiLGYg/MDDwgNgH8GlhgzF4gFoYZ4C0AIUO4NOD0AKyiAcmhFeLRPLDD4w5dvn27LwHH9u23ZHhn9/AePgDXi1pxhKM25Ite5j5ko1z257xSBwj5DCJHAagFmYDHmYeM+nctsM8BgT9IpHD/INxWz1EiyWRWtiAthyGaGEkSgvPMzOLxG3HDXgO8xgb9pw7DPRLYsOBM3i08LMnP77xcVu1AXv/GcMHP8oO2/M3Hz78oQKPFjBIQOUyNhDSMApGwSgYBaOAAAAAFRxAU9eLqJwAAAAASUVORK5CYII=","orcid":"","institution":"University of Catania","correspondingAuthor":true,"prefix":"","firstName":"Luca","middleName":"","lastName":"Martino","suffix":""},{"id":604027665,"identity":"be2a8c7b-71eb-4184-b740-6d3761f5209a","order_by":1,"name":"Francesco Alì","email":"","orcid":"","institution":"KOEXAI s.r.l. 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