{"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":1791558558943,"version":"4.3.4"},"reference-count":63,"publisher":"Institute of Mathematical Statistics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Ann. Statist."],"published-print":{"date-parts":[[2026,6,1]]},"abstract":"Stick-breaking has a long history and is one of the most popular procedures for constructing random discrete distributions in statistics and machine learning. In particular, due to their intuitive construction and computational tractability they are ubiquitous in modern Bayesian nonparametric inference. Most widely used models, such as the Dirichlet and the Pitman\u2013Yor processes, rely on i.i.d. or independent length variables. Here, we pursue a completely unexplored research direction by considering Markov length variables and investigate the corresponding general class of stick-breaking processes, which we term Markov stick-breaking processes. We establish conditions under which the associated species sampling process is proper and the distribution of a Markov stick-breaking process has full topological support, two fundamental desiderata for Bayesian nonparametric models. We also analyze the stochastic ordering of the weights and provide a new characterization of the Pitman\u2013Yor process as the only stick-breaking process invariant under size-biased permutations, under mild conditions. Moreover, we identify two notable subclasses of Markov stick-breaking processes that enjoy appealing properties and include Dirichlet, Pitman\u2013Yor and geometric priors as special cases. Our findings include distributional results enabling posterior inference algorithms and methodological insights.<\/jats:p>","DOI":"10.1214\/25-aos2607","type":"journal-article","created":{"date-parts":[[2026,6,25]],"date-time":"2026-06-25T13:49:23Z","timestamp":1782395363000},"page":"1345-1371","source":"Crossref","is-referenced-by-count":1,"title":["Markov stick-breaking processes"],"prefix":"10.1214","volume":"54","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0811-5083","authenticated-orcid":false,"given":"Mar\u00eda F.","family":"Gil-Leyva","sequence":"first","affiliation":[{"name":"Department of Probability and Statistics, IIMAS, UNAM"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6159-2650","authenticated-orcid":false,"given":"Antonio","family":"Lijoi","sequence":"additional","affiliation":[{"name":"Bocconi Institute for Data Science and Analytics, Bocconi University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9608-8059","authenticated-orcid":false,"given":"Rams\u00e9s H.","family":"Mena","sequence":"additional","affiliation":[{"name":"Department of Probability and Statistics, IIMAS, UNAM"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2860-1476","authenticated-orcid":false,"given":"Igor","family":"Pr\u00fcnster","sequence":"additional","affiliation":[{"name":"Bocconi Institute for Data Science and Analytics, Bocconi University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"108","reference":[{"key":"32","doi-asserted-by":"publisher","unstructured":"Kingman, J. 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