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Moreover, each data point may be accompanied by some additional covariate information and one may be interested in assessing the effect of these covariates on network structure within the population. 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 describe a model for when the outcome of interest is a network-valued random variable whose distribution is given by an exponential random graph model. To perform inference, we implement an exchange-within-Gibbs MCMC algorithm that generates samples from the doubly-intractable posterior. To illustrate this approach, we use it to assess population-level variations in networks derived from fMRI scans, enabling the inference of age- and intelligence-related differences in the topological structure of the brain\u2019s functional connectivity.<\/jats:p>","DOI":"10.1007\/s11222-024-10446-0","type":"journal-article","created":{"date-parts":[[2024,6,19]],"date-time":"2024-06-19T10:02:59Z","timestamp":1718791379000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Bayesian multilevel model for populations of networks using exponential-family random graphs"],"prefix":"10.1007","volume":"34","author":[{"given":"Brieuc","family":"Lehmann","sequence":"first","affiliation":[]},{"given":"Simon","family":"White","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,6,19]]},"reference":[{"issue":"1","key":"10446_CR1","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1523\/jneurosci.3874-05.2006","volume":"26","author":"S Achard","year":"2006","unstructured":"Achard, S., Salvador, R., Whitcher, B., Suckling, J., Bullmore, E.: A resilient, low-frequency, small-world human brain functional network with highly connected association cortical hubs. 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