Bhattacharya (2021) has introduced a novel methodology for generating iid realizations from any target distribution on the Euclidean space, irrespective of dimensionality. In this article, our purpose is two-fold. We first extend the method for obtaining iid realizations from general multimodal distributions, and illustrate with a mixture of two 50-dimensional normal distributions. Then we extend the iid sampling method for fixed-dimensional distributions to variable-dimensional situations and illustrate with a variable-dimensional normal mixture modeling of the well-known "acidity data", with crucial application of the iid sampling method developed for multimodal distributions.

翻译：Bhattacharya(2021年)引进了一种新的方法,从欧几里德空间的任何目标分布中产生iID实现,而不管其维度如何。在本条中,我们的目的是双重的。我们首先扩展了从一般多式联运分布中获得iID实现的方法,并用两种50维正常分布的混合物加以说明。然后,我们将固定维分布的iid抽样方法扩大到多维情况,并以众所周知的“酸性数据”的可变维常态混合模型加以说明,并关键应用为多式联运分布开发的iid抽样方法。