MULTIPARAMETER BERNOULLI FACTORIES

• 成果类型: Article
• 署名作者: Leme, Renato Paes; Schneider, Jon
• 署名单位: Alphabet Inc.; Google Incorporated
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/22-AAP1913
• 发表日期: 2023
• 页码: 3987-4007
• 关键词: coins

摘要

We consider the problem of computing with many coins of unknown bias. We are given access to samples of n coins with unknown biases p1, . . . , pn and are asked to sample from a coin with bias f (p1, ... , pn) for a given function f : [0, 1]n -> [0, 1]. We give a complete characterization of the functions f for which this is possible. As a consequence, we show how to extend various combinatorial sampling procedures (most notably, the classic Sampford sampling for k-subsets) to the boundary of the hypercube.