{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,11,28]],"date-time":"2024-11-28T05:37:00Z","timestamp":1732772220104,"version":"3.29.0"},"reference-count":11,"publisher":"Walter de Gruyter GmbH","issue":"4","license":[{"start":{"date-parts":[[2024,9,21]],"date-time":"2024-09-21T00:00:00Z","timestamp":1726876800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/X027872\/1","EP\/X028119\/1"],"award-info":[{"award-number":["EP\/X027872\/1","EP\/X028119\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100014013","name":"UK Research and Innovation","doi-asserted-by":"publisher","award":["EP\/Y014650\/1"],"award-info":[{"award-number":["EP\/Y014650\/1"]}],"id":[{"id":"10.13039\/100014013","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["20720220046"],"award-info":[{"award-number":["20720220046"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,12,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>This paper aims to address the Bernoulli factory problem of <jats:inline-formula>\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:mn>2<\/m:mn>\n                              <m:mo>\u2062<\/m:mo>\n                              <m:mi mathvariant=\"monospace\">p<\/m:mi>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_mcma-2024-2016_ineq_0001.png\"\/>\n                        <jats:tex-math>2\\mathtt{p}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> coins by analysing the relationship between the negative binomial distributions and binomial distributions generated on the same chain of coin flips.\nThe proposed algorithm requires fewer conditions on the constructed sequences compared with the existing algorithms.\nThe feasibility of obtaining such <jats:inline-formula>\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:mn>2<\/m:mn>\n                              <m:mo>\u2062<\/m:mo>\n                              <m:mi mathvariant=\"monospace\">p<\/m:mi>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_mcma-2024-2016_ineq_0001.png\"\/>\n                        <jats:tex-math>2\\mathtt{p}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>-coin based on \ud835\ude99-coins will be considered as well.<\/jats:p>","DOI":"10.1515\/mcma-2024-2016","type":"journal-article","created":{"date-parts":[[2024,11,27]],"date-time":"2024-11-27T21:10:02Z","timestamp":1732741802000},"page":"365-374","source":"Crossref","is-referenced-by-count":0,"title":["Bernoulli factory: The 2\ud835\ude99-coin problem"],"prefix":"10.1515","volume":"30","author":[{"given":"Shenggang","family":"Hu","sequence":"first","affiliation":[{"name":"Department of Statistics , University of Warwick , Coventry , CV4 7AL , United Kingdom"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bo","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering , Tsinghua University , Beijing , 100084 , P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hongsheng","family":"Dai","sequence":"additional","affiliation":[{"name":"School of Mathematics, Statistics and Physics , Newcastle University , Newcastle upon Tyne , NE1 7RU , United Kingdom"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wei","family":"Liang","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences , Xiamen University , Xiamen , 361005 , United Kingdom"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2024,9,21]]},"reference":[{"key":"2024112721095537578_j_mcma-2024-2016_ref_001","doi-asserted-by":"crossref","unstructured":"G. E. Andrews, R. Askey and R. Roy,\nSpecial Functions,\nEncyclopedia Math. Appl. 71,\nCambridge University, Cambridge, 1999.","DOI":"10.1017\/CBO9781107325937"},{"key":"2024112721095537578_j_mcma-2024-2016_ref_002","doi-asserted-by":"crossref","unstructured":"J. M. Flegal and R. Herbei,\nExact sampling for intractable probability distributions via a Bernoulli factory,\nElectron. J. Stat. 6 (2012), 10\u201337.","DOI":"10.1214\/11-EJS663"},{"key":"2024112721095537578_j_mcma-2024-2016_ref_003","doi-asserted-by":"crossref","unstructured":"R. Herbei and L. M. Berliner,\nEstimating ocean circulation: An MCMC approach with approximated likelihoods via the Bernoulli factory,\nJ. Amer. Statist. Assoc. 109 (2014), no. 507, 944\u2013954.","DOI":"10.1080\/01621459.2014.914439"},{"key":"2024112721095537578_j_mcma-2024-2016_ref_004","doi-asserted-by":"crossref","unstructured":"M. Huber,\nNearly optimal Bernoulli factories for linear functions,\nCombin. Probab. Comput. 25 (2016), no. 4, 577\u2013591.","DOI":"10.1017\/S0963548315000371"},{"key":"2024112721095537578_j_mcma-2024-2016_ref_005","doi-asserted-by":"crossref","unstructured":"M. Huber,\nOptimal linear Bernoulli factories for small mean problems,\nMethodol. Comput. Appl. Probab. 19 (2017), no. 2, 631\u2013645.","DOI":"10.1007\/s11009-016-9518-3"},{"key":"2024112721095537578_j_mcma-2024-2016_ref_006","doi-asserted-by":"crossref","unstructured":"M. S. Keane and G. L. O\u2019Brien,\nA Bernoulli factory,\nACM Trans. Model. Comput. Simul. 4 (1994), no. 2, 213\u2013219.","DOI":"10.1145\/175007.175019"},{"key":"2024112721095537578_j_mcma-2024-2016_ref_007","doi-asserted-by":"crossref","unstructured":"K. \u0141atuszy\u0144ski, I. Kosmidis, O. Papaspiliopoulos and G. O. Roberts,\nSimulating events of unknown probabilities via reverse time martingales,\nRandom Structures Algorithms 38 (2011), no. 4, 441\u2013452.","DOI":"10.1002\/rsa.20333"},{"key":"2024112721095537578_j_mcma-2024-2016_ref_008","doi-asserted-by":"crossref","unstructured":"E. Mossel and Y. Peres,\nNew coins from old: Computing with unknown bias,\nCombinatorica 25 (2005), no. 6, 707\u2013724.","DOI":"10.1007\/s00493-005-0043-1"},{"key":"2024112721095537578_j_mcma-2024-2016_ref_009","doi-asserted-by":"crossref","unstructured":"\u015e. Nacu and Y. Peres,\nFast simulation of new coins from old,\nAnn. Appl. Probab. 15 (2005), no. 1A, 93\u2013115.","DOI":"10.1214\/105051604000000549"},{"key":"2024112721095537578_j_mcma-2024-2016_ref_010","doi-asserted-by":"crossref","unstructured":"P. R. Rider,\nClassroom notes: The negative binomial distribution and the incomplete beta function,\nAmer. Math. Monthly 69 (1962), no. 4, 302\u2013304.","DOI":"10.2307\/2312952"},{"key":"2024112721095537578_j_mcma-2024-2016_ref_011","doi-asserted-by":"crossref","unstructured":"D. Vats, F. B. Gon\u00e7alves, K. \u0141 atuszy\u0144ski and G. O. Roberts,\nEfficient Bernoulli factory Markov chain Monte Carlo for intractable posteriors,\nBiometrika 109 (2022), no. 2, 369\u2013385.","DOI":"10.1093\/biomet\/asab031"}],"container-title":["Monte Carlo Methods and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2024-2016\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2024-2016\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,11,27]],"date-time":"2024-11-27T21:10:50Z","timestamp":1732741850000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2024-2016\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9,21]]},"references-count":11,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2024,11,14]]},"published-print":{"date-parts":[[2024,12,1]]}},"alternative-id":["10.1515\/mcma-2024-2016"],"URL":"https:\/\/doi.org\/10.1515\/mcma-2024-2016","relation":{},"ISSN":["0929-9629","1569-3961"],"issn-type":[{"value":"0929-9629","type":"print"},{"value":"1569-3961","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,9,21]]}}}