{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:26:35Z","timestamp":1750307195395,"version":"3.41.0"},"reference-count":5,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[2012,3,1]],"date-time":"2012-03-01T00:00:00Z","timestamp":1330560000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Model. Comput. Simul."],"published-print":{"date-parts":[[2012,3]]},"abstract":"<jats:p>\n            Given a black box that generates independent Bernoulli samples with an unknown bias p, we consider the problem of simulating a Bernoulli random variable with bias\n            <jats:italic>f<\/jats:italic>\n            (\n            <jats:italic>p<\/jats:italic>\n            ) (where\n            <jats:italic>f<\/jats:italic>\n            is a given function) using a finite (computable in advance) number of independent Bernoulli samples from the black box. We show that this is possible if and only if\n            <jats:italic>f<\/jats:italic>\n            is a Bernstein polynomial with coefficients between 0 and 1, and we explicitly give the algorithm. Our results differ from Keane and O'Brien [1994] in that our goal is more modest\/stringent, since we are considering algorithms that use a\n            <jats:italic>finite<\/jats:italic>\n            number of samples as opposed to allowing a random number (such as in acceptance rejection algorithms).\n          <\/jats:p>","DOI":"10.1145\/2133390.2133396","type":"journal-article","created":{"date-parts":[[2012,3,27]],"date-time":"2012-03-27T15:17:31Z","timestamp":1332861451000},"page":"1-5","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":4,"title":["On simulating a class of Bernstein polynomials"],"prefix":"10.1145","volume":"22","author":[{"given":"Vineet","family":"Goyal","sequence":"first","affiliation":[{"name":"Columbia University, New York, NY"}]},{"given":"Karl","family":"Sigman","sequence":"additional","affiliation":[{"name":"Columbia University, New York, NY"}]}],"member":"320","published-online":{"date-parts":[[2012,3,30]]},"reference":[{"key":"e_1_2_1_1_1","volume-title":"Stochastic Simulation: Algorithms and Analysis","author":"Asmussen S.","year":"2008","unstructured":"Asmussen , S. and Glynn , P . 2008 . Stochastic Simulation: Algorithms and Analysis . Springer , New York . Asmussen, S. and Glynn, P. 2008. Stochastic Simulation: Algorithms and Analysis. Springer, New York."},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/175007.175019"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1214\/105051604000000549"},{"key":"e_1_2_1_4_1","first-page":"36","article-title":"Various techniques used in connection with random digits","volume":"12","author":"Neumann J.","year":"1951","unstructured":"Neumann , J. 1951 . Various techniques used in connection with random digits . Nat. Bureau Standards, Appl. Math. Series 12 , 36 -- 38 . Neumann, J. 1951. Various techniques used in connection with random digits. Nat. Bureau Standards, Appl. Math. Series 12, 36--38.","journal-title":"Nat. Bureau Standards, Appl. Math. Series"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176348543"}],"container-title":["ACM Transactions on Modeling and Computer Simulation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2133390.2133396","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2133390.2133396","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T10:06:05Z","timestamp":1750241165000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2133390.2133396"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,3]]},"references-count":5,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2012,3]]}},"alternative-id":["10.1145\/2133390.2133396"],"URL":"https:\/\/doi.org\/10.1145\/2133390.2133396","relation":{},"ISSN":["1049-3301","1558-1195"],"issn-type":[{"type":"print","value":"1049-3301"},{"type":"electronic","value":"1558-1195"}],"subject":[],"published":{"date-parts":[[2012,3]]},"assertion":[{"value":"2011-04-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2011-10-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-03-30","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}