{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/clarifying-the-hubble-constant-tension-with-a","title":"Clarifying the Hubble constant tension with a Bayesian hierarchical model of the local distance ladder","arxiv_id":"1707.00007","date":"2017-06-30","proceeding":null,"authors":["Stephen M. Feeney","Daniel J. Mortlock","Niccolò Dalmasso"],"abstract":"Estimates of the Hubble constant, $H_0$, from the distance ladder and the cosmic microwave background (CMB) differ at the $\\sim$3-$\\sigma$ level, indicating a potential issue with the standard $\\Lambda$CDM cosmology. Interpreting this tension correctly requires a model comparison calculation depending on not only the traditional `$n$-$\\sigma$' mismatch but also the tails of the likelihoods. Determining the form of the tails of the local $H_0$ likelihood is impossible with the standard Gaussian least-squares approximation, as it requires using non-Gaussian distributions to faithfully represent anchor likelihoods and model outliers in the Cepheid and supernova (SN) populations, and simultaneous fitting of the full distance-ladder dataset to correctly propagate uncertainties. We have developed a Bayesian hierarchical model that describes the full distance ladder, from nearby geometric anchors through Cepheids to Hubble-Flow SNe. This model does not rely on any distributions being Gaussian, allowing outliers to be modeled and obviating the need for arbitrary data cuts. Sampling from the $\\sim$3000-parameter joint posterior using Hamiltonian Monte Carlo, we find $H_0$ = (72.72 $\\pm$ 1.67) ${\\rm km\\,s^{-1}\\,Mpc^{-1}}$ when applied to the outlier-cleaned Riess et al. (2016) data, and ($73.15 \\pm 1.78$) ${\\rm km\\,s^{-1}\\,Mpc^{-1}}$ with SN outliers reintroduced. Our high-fidelity sampling of the low-$H_0$ tail of the distance-ladder likelihood allows us to apply Bayesian model comparison to assess the evidence for deviation from $\\Lambda$CDM. We set up this comparison to yield a lower limit on the odds of the underlying model being $\\Lambda$CDM given the distance-ladder and Planck XIII (2016) CMB data. The odds against $\\Lambda$CDM are at worst 10:1 or 7:1, depending on whether the SNe outliers are cut or modeled, or 60:1 if an approximation to the Planck Int. XLVI (2016) likelihood is used.","url_abs":"http://arxiv.org/abs/1707.00007v2","url_pdf":"http://arxiv.org/pdf/1707.00007v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"clarifying-the-hubble-constant-tension-with-a","repo_url":"https://github.com/sfeeney/hh0","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}