{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T15:09:18Z","timestamp":1791558558181,"version":"4.3.4"},"reference-count":43,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2007,8,7]],"date-time":"2007-08-07T00:00:00Z","timestamp":1186444800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"name":"Italian Ministry of University and Research","award":["2006134525"],"award-info":[{"award-number":["2006134525"]}]},{"name":"Italian Ministry of University and Research","award":["2006133449"],"award-info":[{"award-number":["2006133449"]}]},{"DOI":"10.13039\/501100003141","name":"Consejo Nacional de Ciencia y Tecnolog\u00eda, M\u00e9xico","doi-asserted-by":"publisher","award":["J50160-F"],"award-info":[{"award-number":["J50160-F"]}],"id":[{"id":"10.13039\/501100003141","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2007,9,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>The paper deals with the problem of determining the number of components in a mixture model. We take a Bayesian non-parametric approach and adopt a hierarchical model with a suitable non-parametric prior for the latent structure. A commonly used model for such a problem is the mixture of Dirichlet process model. Here, we replace the Dirichlet process with a more general non-parametric prior obtained from a generalized gamma process. The basic feature of this model is that it yields a partition structure for the latent variables which is of Gibbs type. This relates to the well-known (exchangeable) product partition models. If compared with the usual mixture of Dirichlet process model the advantage of the generalization that we are examining relies on the availability of an additional parameter \u03c3 belonging to the interval (0,1): it is shown that such a parameter greatly influences the clustering behaviour of the model. A value of \u03c3 that is close to 1 generates a large number of clusters, most of which are of small size. Then, a reinforcement mechanism which is driven by \u03c3 acts on the mass allocation by penalizing clusters of small size and favouring those few groups containing a large number of elements. These features turn out to be very useful in the context of mixture modelling. Since it is difficult to specify a priori the reinforcement rate, it is reasonable to specify a prior for \u03c3. Hence, the strength of the reinforcement mechanism is controlled by the data.<\/jats:p>","DOI":"10.1111\/j.1467-9868.2007.00609.x","type":"journal-article","created":{"date-parts":[[2007,8,7]],"date-time":"2007-08-07T10:05:31Z","timestamp":1186481131000},"page":"715-740","source":"Crossref","is-referenced-by-count":166,"title":["Controlling the Reinforcement in Bayesian Non-Parametric Mixture Models"],"prefix":"10.1093","volume":"69","author":[{"given":"Antonio","family":"Lijoi","sequence":"first","affiliation":[{"name":"Universit\u00e0 degli Studi di Pavia , Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rams\u00e9s H.","family":"Mena","sequence":"additional","affiliation":[{"name":"Universidad Nacional Aut\u00f3noma de M\u00e9xico , Mexico City , Mexico"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Igor","family":"Pr\u00fcnster","sequence":"additional","affiliation":[{"name":"Universit\u00e0 degli Studi di Torino ,"},{"name":"Collegio Carlo Alberto ,"},{"name":"International Centre for Economic Research , Turin , Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2007,8,7]]},"reference":[{"key":"2023040704574289400_","doi-asserted-by":"crossref","first-page":"1152","DOI":"10.1214\/aos\/1176342871","article-title":"Mixtures of Dirichlet processes with applications to Bayesian non-parametric problems","volume":"2","author":"Antoniak","year":"1974","journal-title":"Ann. 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