{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,22]],"date-time":"2026-07-22T07:49:30Z","timestamp":1784706570948,"version":"3.55.0"},"reference-count":49,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2023,1,30]],"date-time":"2023-01-30T00:00:00Z","timestamp":1675036800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,2,27]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>There has been considerable interest in addressing the problem of unifying distributed analyses into a single coherent inference, which arises in big-data settings, when working under privacy constraints, and in Bayesian model choice. Most existing approaches relied upon approximations of the distributed analyses, which have significant shortcomings\u2014the quality of the inference can degrade rapidly with the number of analyses being unified, and can be substantially biased when unifying analyses that do not concur. In contrast, recent Monte Carlo fusion approach is exact and based on rejection sampling. In this paper, we introduce a practical Bayesian fusion approach by embedding the Monte Carlo fusion framework within a sequential Monte Carlo algorithm. We demonstrate theoretically and empirically that Bayesian fusion is more robust than existing methods.<\/jats:p>","DOI":"10.1093\/jrsssb\/qkac007","type":"journal-article","created":{"date-parts":[[2023,1,30]],"date-time":"2023-01-30T12:17:11Z","timestamp":1675081031000},"page":"84-107","source":"Crossref","is-referenced-by-count":11,"title":["Bayesian fusion: scalable unification of distributed statistical analyses"],"prefix":"10.1093","volume":"85","author":[{"given":"Hongsheng","family":"Dai","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, University of Essex , Colchester ,","place":["UK"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Murray","family":"Pollock","sequence":"additional","affiliation":[{"name":"School of Mathematics, Statistics and Physics, Newcastle University , Newcastle-upon-Tyne ,","place":["UK"]},{"name":"The Alan Turing Institute , London ,","place":["UK"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gareth O","family":"Roberts","sequence":"additional","affiliation":[{"name":"The Alan Turing Institute , London ,","place":["UK"]},{"name":"Department of Statistics, University of Warwick , Coventry ,","place":["UK"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2023,1,30]]},"reference":[{"key":"2024110513562351100_qkac007-B1","author":"Agarwal","year":"2011"},{"key":"2024110513562351100_qkac007-B2","doi-asserted-by":"crossref","first-page":"697","DOI":"10.1214\/07-AOS574","article-title":"The pseudo-marginal approach for efficient Monte Carlo computations","volume":"37","author":"Andrieu","year":"2009","journal-title":"Annals of Statistics"},{"key":"2024110513562351100_qkac007-B3","author":"Bache","year":"2013"},{"key":"2024110513562351100_qkac007-B4","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-1727-3","volume-title":"Statistical decision theory and Bayesian analysis","author":"Berger","year":"1980"},{"key":"2024110513562351100_qkac007-B5","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1007\/s11009-007-9060-4","article-title":"A factorisation of diffusion measure and finite sample path constructions","volume":"10","author":"Beskos","year":"2008","journal-title":"Methodology and Computing in Applied Probability"},{"issue":"4","key":"2024110513562351100_qkac007-B6","doi-asserted-by":"crossref","first-page":"2422","DOI":"10.1214\/105051605000000485","article-title":"An exact simulation of diffusions","volume":"15","author":"Beskos","year":"2005","journal-title":"Annals of Applied Probability"},{"issue":"7","key":"2024110513562351100_qkac007-B7","doi-asserted-by":"crossref","first-page":"2442","DOI":"10.1109\/TSP.2005.849185","article-title":"Resampling algorithms and architectures for distributed particle filters","volume":"53","author":"Bolic","year":"2005","journal-title":"IEEE Transactions on Signal Processing"},{"key":"2024110513562351100_qkac007-B8","author":"Buchholz","year":"2019"},{"key":"2024110513562351100_qkac007-B9","author":"Chan","year":"2021"},{"key":"2024110513562351100_qkac007-B10","doi-asserted-by":"crossref","first-page":"2054","DOI":"10.1214\/13-EJS837","article-title":"The Polya-Gamma Gibbs sampler for Bayesian logistic regression is uniformly ergodic","volume":"7","author":"Choi","year":"2013","journal-title":"Electronic Journal of Statistics"},{"key":"2024110513562351100_qkac007-B11","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1017\/jpr.2019.12","article-title":"Monte Carlo Fusion","volume":"56","author":"Dai","year":"2019","journal-title":"Journal of Applied Probability"},{"key":"2024110513562351100_qkac007-B12","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1111\/biom.12121","article-title":"Fully Bayesian inference under ignorable missingness in the presence of auxiliary covariates","volume":"70","author":"Daniels","year":"2013","journal-title":"Biometrics"},{"key":"2024110513562351100_qkac007-B13","volume-title":"Feynman-Kac formulae. 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