{"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/dirichlet-process-mixtures-of-block-g-priors","title":"Dirichlet process mixtures of block $g$ priors for model selection and prediction in linear models","arxiv_id":"2411.00471","date":"2024-11-01","proceeding":null,"authors":["Anupreet Porwal","Abel Rodriguez"],"abstract":"This paper introduces Dirichlet process mixtures of block $g$ priors for model selection and prediction in linear models. These priors are extensions of traditional mixtures of $g$ priors that allow for differential shrinkage for various (data-selected) blocks of parameters while fully accounting for the predictors' correlation structure, providing a bridge between the literatures on model selection and continuous shrinkage priors. We show that Dirichlet process mixtures of block $g$ priors are consistent in various senses and, in particular, that they avoid the conditional Lindley ``paradox'' highlighted by Som et al.(2016). Further, we develop a Markov chain Monte Carlo algorithm for posterior inference that requires only minimal ad-hoc tuning. Finally, we investigate the empirical performance of the prior in various real and simulated datasets. In the presence of a small number of very large effects, Dirichlet process mixtures of block $g$ priors lead to higher power for detecting smaller but significant effects without only a minimal increase in the number of false discoveries.","url_abs":"https://arxiv.org/abs/2411.00471v1","url_pdf":"https://arxiv.org/pdf/2411.00471v1.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":"abstracts"},"code_links":[{"paper_slug":"dirichlet-process-mixtures-of-block-g-priors","repo_url":"https://github.com/Anupreet-Porwal/DP-mix-block-g-prior","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"model-selection","task_name":"Model Selection"}],"methods":[{"method_slug":"som","method_name":"SOM"}],"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}