{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,23]],"date-time":"2026-10-23T20:03:21Z","timestamp":1792785801756,"version":"4.5.0"},"reference-count":50,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T00:00:00Z","timestamp":1771459200000},"content-version":"vor","delay-in-days":49,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Research Grants Council of Hong Kong through the Early Career Scheme","award":["27304424"],"award-info":[{"award-number":["27304424"]}]},{"name":"General Research Fund","award":["17306925"],"award-info":[{"award-number":["17306925"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,2,13]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>The martingale posterior framework replaces the elicitation of the likelihood and prior with that of a sequence of one-step-ahead predictive densities for Bayesian inference. Posterior sampling then involves the imputation of unobserved quantities and can then be carried out in an expedient and parallelizable manner using predictive resampling, without requiring Markov chain Monte Carlo. Recent work has investigated the use of plug-in parametric predictive densities, combined with stochastic gradient descent, to specify a parametric martingale posterior. This paper investigates the asymptotic properties of this class of parametric martingale posteriors. In particular, two central limit theorems based on martingale limit theory are introduced and applied. The first is a predictive central limit theorem, which enables a significant acceleration of the predictive resampling scheme through a hybrid sampling algorithm based on a normal approximation. The second is a Bernstein\u2013von Mises result, which is novel for martingale posteriors, and provides methodological guidance on attaining desirable frequentist properties. We demonstrate the utility of the theoretical results through simulations and a real data example.<\/jats:p>","DOI":"10.1093\/biomet\/asag007","type":"journal-article","created":{"date-parts":[[2026,1,30]],"date-time":"2026-01-30T12:40:16Z","timestamp":1769776816000},"source":"Crossref","is-referenced-by-count":6,"title":["Asymptotics for a class of parametric martingale posteriors"],"prefix":"10.1093","volume":"113","author":[{"given":"E","family":"Fong","sequence":"first","affiliation":[{"name":"Department of Statistics and Actuarial Science, University of Hong Kong , Pokfulam, \u00a0 chefong@hku.hk","place":["Hong Kong"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"A.","family":"Yiu","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, University of Southampton , University Road , Southampton SO17 1BJ, . a.h.m.yiu@soton.ac.uk","place":["U.K"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2026,2,19]]},"reference":[{"key":"2026042200213693400_asag007-B1","author":"Asuncion","year":"2007"},{"key":"2026042200213693400_asag007-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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