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Building on a quasi-Bayesian approach based on Newton\u2019s algorithm, we develop a sequential estimate that is easy to evaluate, computationally efficient and has constant per-observation cost as the data accrue. We establish frequentist guarantees for the proposed estimate, including consistency and asymptotic optimality, with optimality understood as vanishing excess Bayes risk, or regret. Empirical performance is assessed through simulation studies and comparisons with benchmark procedures.<\/jats:p>","DOI":"10.1093\/biomet\/asag037","type":"journal-article","created":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T12:26:00Z","timestamp":1781612760000},"source":"Crossref","is-referenced-by-count":0,"title":["Quasi-Bayes empirical Bayes: a sequential approach to the Poisson compound decision problem"],"prefix":"10.1093","volume":"113","author":[{"given":"S","family":"Favaro","sequence":"first","affiliation":[{"name":"Department of Economics and Statistics, University of Torino and Collegio Carlo Alberto , Corso Unione Sovietica 218\/bis , 10134 Torino, \u00a0 stefano.favaro@unito.it","place":["Italy"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"S","family":"Fortini","sequence":"additional","affiliation":[{"name":"Department of Decision Sciences, Bocconi University , Via R\u00f6ntgen 1 , 20136 Milano, sandra.fortini@unibocconi.it","place":["Italy"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2026,6,18]]},"reference":[{"key":"2026080308113124800_asag037-B1","author":"Battiston","year":"2025"},{"key":"2026080308113124800_asag037-B2","doi-asserted-by":"crossref","first-page":"2029","DOI":"10.1214\/009117904000000676","article-title":"Limit theorems for a class of identically distributed random variables","volume":"32","author":"Berti","year":"2004","journal-title":"Ann. 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