We propose a novel methodology for drawing iid realizations from any target distribution on the Euclidean space with arbitrary dimension. No assumption of compact support is necessary for the validity of our theory and method. Our idea is to construct an appropriate infinite sequence of concentric closed ellipsoids, represent the target distribution as an infinite mixture on the central ellipsoid and the ellipsoidal annuli, and to construct efficient perfect samplers for the mixture components. In contrast with most of the existing works on perfect sampling, ours is not only a theoretically valid method, it is practically applicable to all target distributions on any dimensional Euclidean space and very much amenable to parallel computation. We validate the practicality and usefulness of our methodology by generating 10000 iid realizations from the standard distributions such as normal, Student's t with 5 degrees of freedom and Cauchy, for dimensions d = 1, 5, 10, 50, 100, as well as from a 50-dimensional mixture normal distribution. The implementation time in all the cases are very reasonable, and often less than a minute in our parallel implementation. The results turned out to be highly accurate. We also apply our method to draw 10000 iid realizations from the posterior distributions associated with the well-known Challenger data, a Salmonella data and the 160-dimensional challenging spatial example of the radionuclide count data on Rongelap Island. Again, we are able to obtain quite encouraging results with very reasonable computing time.

翻译：本文提出一种从任意维度欧几里得空间上的目标分布中抽取独立同分布实现的新方法。我们的理论和方法有效性无需紧支撑假设。核心思想是构建适当的无穷同心闭合椭球序列，将目标分布表示为中央椭球与椭球环带上的无穷混合分布，并为混合分量构建高效完美采样器。与现有完美采样研究相比，本方法不仅理论严谨，且能实际应用于任意维度欧几里得空间的所有目标分布，并高度适用于并行计算。我们通过从标准分布（正态分布、5自由度t分布、柯西分布）在维度d=1,5,10,50,100的情形，以及50维混合正态分布中生成10000个独立同分布实现，验证了方法的实用性与有效性。所有案例的执行时间均非常合理，在并行实现中通常少于一分钟，且结果精度极高。进一步将方法应用于从著名挑战者号数据、沙门氏菌数据，以及朗格拉普岛放射性核素计数数据这一160维挑战性空间案例的后验分布中抽取10000个独立同分布实现，均在合理计算时间内获得了令人鼓舞的结果。