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We relate their convergence properties to the ones of the corresponding (potentially not implementable) random scan Gibbs sampler through the notion of conditional conductance. This allows us to study the performances of popular Metropolis-within-Gibbs schemes for non-conjugate hierarchical models, in high-dimensional regimes where both number of datapoints and parameters increase. Given random data-generating assumptions, we establish dimension-free convergence results, which are in close accordance with numerical evidences. Application to Bayesian models for binary regression with unknown hyperparameters is also discussed. Motivated by such statistical applications, auxiliary results of independent interest on approximate conductances and perturbation of Markov operators are provided.<\/jats:p>","DOI":"10.1093\/jrsssb\/qkaf084","type":"journal-article","created":{"date-parts":[[2025,12,24]],"date-time":"2025-12-24T12:56:46Z","timestamp":1766581006000},"page":"1231-1250","source":"Crossref","is-referenced-by-count":1,"title":["Scalability of Metropolis-within-Gibbs schemes for high-dimensional Bayesian models"],"prefix":"10.1093","volume":"88","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-3899-8877","authenticated-orcid":false,"given":"Filippo","family":"Ascolani","sequence":"first","affiliation":[{"name":"Department of Statistical Science, Duke University , Durham, NC 27708 ,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gareth O","family":"Roberts","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of Warwick , Coventry CV4 7AL 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