The distributions of toroidal data, often viewed as an extension of circular distributions, do not consider the intrinsic geometry of a curved torus. For the first time, Diaconis et al. (2013)[Diaconis, P., Holmes, S., & Shahshahani, M. (2013). Sampling from a manifold. Advances in modern statistical theory and applications: a Festschrift in honor of Morris L. Eaton, 10, 102-125.] introduce uniform distribution on the surface of a curved torus with respect to its surface area. But the suggested acceptance-rejection method of sampling from it rejects approximately half of the data. We propose a probabilistic transformation for sampling from the same distribution without losing data. In addition, we introduce a new genesis of random samples from some popular circular distributions using histogram-based acceptance-rejection sampling that uses a very thin envelope. The idea leads to generalizing for sampling from distributions on the surface of a curved torus with a high acceptance rate.Apart from reducing computational cost in the inferential study of different toroidal distributions, uniform sampling from the surface of a curve torus will be helpful to understand any unknown distribution on it.
翻译:曲面环面数据分布通常被视为圆形分布的扩展,但是不考虑其固有的几何形状。Diaconis等人(2013)首次介绍了曲面环面上的均匀分布,并针对其表面积提出了一种接受-拒绝采样方法。但是该方法会拒绝近一半的数据。我们提出了一种概率变换方法,可以从相同的分布中进行采样,无需丢失数据。此外,我们还提出了一种基于直方图的接受-拒绝采样方法,用于从一些流行的圆形分布中生成随机样本,该方法使用非常薄的信封。这一想法导致了高接受率的曲面环面分布的采样方法的推广。除了减少推断研究中不同环面分布的计算成本之外,从曲面环面的表面均匀采样将有助于理解其上的任何未知分布。