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:我们提出一种新颖的方法,从欧几里德空间的任何分布目标中任意地提取实现的真象。对于我们的理论和方法的有效性来说,无需假定提供紧凑的支持。我们的想法是构建一个合适的、无限的同心闭足的埃利球体序列,将目标分布作为一种无限的混合物,表现在中央环球体和埃利线脱氧剂中,为混合成分构建高效的完美采样器。与大多数关于完美采样的现有工作相比,我们不仅是一种理论上有效的方法,而且实际上适用于任何方位欧几里德空间的所有目标分布,而且非常适合平行计算。我们的想法是,我们验证我们方法的实用性和有用性,从正常的分布中产生10 000个异象,学生自由度为5度,卡奥利特,尺寸为1,5,10,50,100,以及50维利特混合成分的正常分布。所有案例的执行时间都非常合理,而且往往比我们平行执行的欧洲大陆空间空间空间空间空间空间分布要短一分钟。我们用的方法验证出一个非常准确的160号数据。我们实现一个非常精确的地图。我们的方法,同样也用一个非常精确地反映了。