We derive a probability distribution for the possible number of iterations required for a SIMT (single instruction multiple thread) program using rejection sampling to finish creating a sample across all threads. This distribution is found to match a recently proposed distribution from Chakraborty and Gupta (in: Communications in statistics: theory and methods, 2015) that was shown as a good approximation of certain datasets. This work demonstrates an exact application of this distribution. The distribution can be used to evaluate the relative merit of some sampling methods on the GPU without resort to numerical tests. The distribution reduces to the expected geometric distribution in the single thread per warp limit. A simplified formula to approximate the expected number of iterations required to obtain rejection iteration samples is provided. With this new result, a simple, efficient layout for assigning sampling tasks to threads on a GPU is found as a function of the rejection probability without recourse to more complicated rejection sampling methods.

我们使用拒绝采样来完成SIMT（单指令多线程）程序所需的可能迭代次数的概率分布，以完成所有线程之间的样本创建。发现此分布与Chakraborty和Gupta最近提出的分布（在《统计学中的通信：理论和方法》，2015年）中相匹配，该分布显示为某些数据集的良好近似。这项工作演示了此发行版的确切应用。该分布可用于评估GPU上某些采样方法的相对价值，而无需进行数值测试。该分布减少到每个经纱极限在单线中的预期几何分布。提供了一个简化的公式，用于近似估计获得拒绝迭代样本所需的预期迭代次数。