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Under some balancedness conditions on the data designs and assuming that precision hyperparameters are known, we demonstrate that the plain Gibbs sampler is not scalable, in the sense that its complexity is worse than proportional to the number of parameters and data, but the collapsed Gibbs sampler is scalable. In simulated and real datasets we show that the explicit convergence rates predicted by our theory closely match the computable, but nonexplicit rates in cases where the design assumptions are violated. We also show empirically that the collapsed Gibbs sampler extended to sample precision hyperparameters significantly outperforms alternative state-of-the-art algorithms.<\/jats:p>","DOI":"10.1093\/biomet\/asz058","type":"journal-article","created":{"date-parts":[[2019,9,27]],"date-time":"2019-09-27T00:33:19Z","timestamp":1569544399000},"source":"Crossref","is-referenced-by-count":15,"title":["Scalable inference for crossed random effects models"],"prefix":"10.1093","author":[{"given":"O","family":"Papaspiliopoulos","sequence":"first","affiliation":[{"name":"Instituci\u00f3 Catalana de Recerca i Estudis Avan\u00e7ats, Ramon Trias Fargas 25-27, Barcelona 08005, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"G O","family":"Roberts","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of Warwick, Coventry CV4 7AL, U.K"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"G","family":"Zanella","sequence":"additional","affiliation":[{"name":"Department of Decision Sciences, BIDSA and IGIER, Bocconi University, Via Roentgen 1, 20136 Milan, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2019,11,15]]},"reference":[{"key":"2019111506503450500_B1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.18637\/jss.v067.i01","article-title":"Fitting linear mixed-effects models using lme4","volume":"67","author":"Bates,","year":"2015","journal-title":"J. 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