{"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/on-the-limits-of-some-bayesian-model","title":"On the limits of some Bayesian model evaluation statistics","arxiv_id":"2502.03846","date":"2025-02-06","proceeding":null,"authors":["Hien Duy Nguyen","Mayetri Gupta","Jacob Westerhout","TrungTin Nguyen"],"abstract":"Model selection and order selection problems frequently arise in statistical practice. A popular approach to addressing these problems in the frequentist setting involves information criteria based on penalised maxima of log-likelihoods for competing models. In the Bayesian context, similar criteria are employed, replacing the maximised log-likelihoods with posterior expectations of the log-likelihood. Despite their popularity in applications, the large-sample behaviour of these criteria -- such as the deviance information criterion (DIC), Bayesian predictive information criterion (BPIC), and widely applicable Bayesian information criterion (WBIC) -- has received relatively little attention. In this work, we investigate the almost-sure limits of these criteria and establish novel results on posterior and generalised posterior consistency, which are of independent interest. The utility of our theoretical findings is demonstrated via illustrative technical and numerical examples.","url_abs":"https://arxiv.org/abs/2502.03846v1","url_pdf":"https://arxiv.org/pdf/2502.03846v1.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":"on-the-limits-of-some-bayesian-model","repo_url":"https://github.com/hiendn/BayesianIC","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"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}