{"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/bayesian-exponential-random-graph-models-for","title":"Bayesian exponential random graph models for populations of networks","arxiv_id":"2104.05110","date":"2021-04-11","proceeding":null,"authors":["Brieuc Lehmann","Simon White"],"abstract":"The collection of data on populations of networks is becoming increasingly common, where each data point can be seen as a realisation of a network-valued random variable. A canonical example is that of brain networks: a typical neuroimaging study collects one or more brain scans across multiple individuals, each of which can be modelled as a network with nodes corresponding to distinct brain regions and edges corresponding to structural or functional connections between these regions. Most statistical network models, however, were originally proposed to describe a single underlying relational structure, although recent years have seen a drive to extend these models to populations of networks. Here, we propose one such extension: a multilevel framework for populations of networks based on exponential random graph models. By pooling information across the individual networks, this framework provides a principled approach to characterise the relational structure for an entire population. To perform inference, we devise a novel exchange-within-Gibbs MCMC algorithm that generates samples from the doubly-intractable posterior. To illustrate our framework, we use it to assess group-level variations in networks derived from fMRI scans, enabling the inference of age-related differences in the topological structure of the brain's functional connectivity.","url_abs":"https://arxiv.org/abs/2104.05110v1","url_pdf":"https://arxiv.org/pdf/2104.05110v1.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":"bayesian-exponential-random-graph-models-for","repo_url":"https://github.com/brieuclehmann/multibergm-scripts","is_official":1,"mentioned_in_paper":1,"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}