{"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/nonparametric-fbst-for-validating-linear","title":"Nonparametric FBST for Validating Linear Models","arxiv_id":"2406.15608","date":"2024-06-21","proceeding":null,"authors":["Rodrigo F. L. Lassance","Julio M. Stern","Rafael B. Stern"],"abstract":"The Full Bayesian Significance Test (FBST) possesses many desirable aspects, such as dismissing the need for hypotheses to have positive prior probability and providing a measure of evidence against $H_0$. Still, few attempts have been made to bring the FBST to nonparametric settings, with the main drawback being the need to obtain the highest posterior density (HPD) in a function space. In this work, we use a Gaussian processes prior to derive the FBST for hypotheses of the type $$ H_0: g(\\boldsymbol{x}) = \\boldsymbol{b}(\\boldsymbol{x})\\boldsymbol{\\beta}, \\quad \\forall \\boldsymbol{x} \\in \\mathcal{X}, \\quad \\boldsymbol{\\beta} \\in \\mathbb{R}^k, $$ where $g(\\cdot)$ is the regression function, $\\boldsymbol{b}(\\cdot)$ is a vector of linearly independent linear functions -- such as $\\boldsymbol{b}(\\boldsymbol{x}) = \\boldsymbol{x}'$ -- and $\\mathcal{X}$ is the covariates' domain. We also make use of pragmatic hypotheses to verify if the data might be compatible with a linear model when factors such as measurement errors or utility judgments are accounted for. This contribution extends the theory of the FBST, allowing its application in nonparametric settings and providing a procedure that easily tests if linear models are adequate for the data and that can automatically perform variable selection.","url_abs":"https://arxiv.org/abs/2406.15608v1","url_pdf":"https://arxiv.org/pdf/2406.15608v1.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":"nonparametric-fbst-for-validating-linear","repo_url":"https://github.com/rflassance/lmfbst","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}