A Practical Implementation of the Bernoulli Factory
A Practical Implementation of the Bernoulli Factory
复制标题
伯努利工厂的实际实现
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
J. Blanchet
中科院分区：
文献类型：
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作者：
Anoop Cherian Thomas;J. Blanchet
伯努利工厂是一种以一系列独立同分布作为输入的算法。具有未知但固定成功概率 $p$ 的伯努利随机变量，并输出具有成功概率 $f(p)$ 的相应伯努利随机变量系列，其中函数 $f$ 已知并在区间 $[0,1]$ 上定义。虽然在蒙特卡罗应用中已经提出了该方法的几种实际用途，但这些用途需要灵活、通用和高效的实现框架。我们使用通过级联定义的一系列包络函数，提出了这样一个在单位间隔上严格线性、凹或凸的函数框架，并且表明，与当前针对更具体问题提出的其他解决方案相比，该方法不仅大大减少了实践中所需的输入位数，而且易于指定简单的形式，而且可以轻松地与渐近有效的方法耦合，以实现理论上强大的结果。
The Bernoulli Factory is an algorithm that takes as input a series of i.i.d. Bernoulli random variables with an unknown but fixed success probability $p$, and outputs a corresponding series of Bernoulli random variables with success probability $f(p)$, where the function $f$ is known and defined on the interval $[0,1]$. While several practical uses of the method have been proposed in Monte Carlo applications, these require an implementation framework that is flexible, general and efficient. We present such a framework for functions that are either strictly linear, concave, or convex on the unit interval using a series of envelope functions defined through a cascade, and show that this method not only greatly reduces the number of input bits needed in practice compared to other currently proposed solutions for more specific problems, and is easy to specify for simple forms, but can easily be coupled to asymptotically efficient methods to allow for theoretically strong results.
影响因子：
1
作者：
Krzysztof Latuszynski;I. Kosmidis;O. Papaspiliopoulos;G. Roberts
通讯作者：
Krzysztof Latuszynski;I. Kosmidis;O. Papaspiliopoulos;G. Roberts