{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T04:00:26Z","timestamp":1793505626758,"version":"4.5.0"},"reference-count":22,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2022,9,12]],"date-time":"2022-09-12T00:00:00Z","timestamp":1662940800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,5,15]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>Dirichlet process mixtures are flexible nonparametric models, particularly suited to density estimation and probabilistic clustering. In this work we study the posterior distribution induced by Dirichlet process mixtures as the sample size increases, and more specifically focus on consistency for the unknown number of clusters when the observed data are generated from a finite mixture. Crucially, we consider the situation where a prior is placed on the concentration parameter of the underlying Dirichlet process. Previous findings in the literature suggest that Dirichlet process mixtures are typically not consistent for the number of clusters if the concentration parameter is held fixed and data come from a finite mixture. Here we show that consistency for the number of clusters can be achieved if the concentration parameter is adapted in a fully Bayesian way, as commonly done in practice. Our results are derived for data coming from a class of finite mixtures, with mild assumptions on the prior for the concentration parameter and for a variety of choices of likelihood kernels for the mixture.<\/jats:p>","DOI":"10.1093\/biomet\/asac051","type":"journal-article","created":{"date-parts":[[2022,9,9]],"date-time":"2022-09-09T19:23:54Z","timestamp":1662751434000},"page":"551-558","source":"Crossref","is-referenced-by-count":41,"title":["Clustering consistency with Dirichlet process mixtures"],"prefix":"10.1093","volume":"110","author":[{"given":"F","family":"Ascolani","sequence":"first","affiliation":[{"name":"Bocconi University Department of Decision Sciences & BIDSA, , via R\u00f6ntgen 1, 20136 Milan, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"A","family":"Lijoi","sequence":"additional","affiliation":[{"name":"Bocconi University Department of Decision Sciences & BIDSA, , via R\u00f6ntgen 1, 20136 Milan, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4619-9302","authenticated-orcid":false,"given":"G","family":"Rebaudo","sequence":"additional","affiliation":[{"name":"University of Texas at Austin Department of Statistics and Data Sciences, , 105 E 24th Street, Austin, Texas 78705, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"G","family":"Zanella","sequence":"additional","affiliation":[{"name":"Bocconi University Department of Decision Sciences, BIDSA & IGIER, , via R\u00f6ntgen 1, 20136 Milan, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2022,9,12]]},"reference":[{"key":"2023051508565297100_B1","doi-asserted-by":"crossref","first-page":"1152","DOI":"10.1214\/aos\/1176342871","article-title":"Mixtures of Dirichlet processes with applications to Bayesian nonparametric problems","volume":"2","author":"Antoniak,","year":"1974","journal-title":"Ann. 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