Probability measures that are constrained to the sphere form an important class of statistical models and are used, for example, in modeling directional data or shapes. Therefore, and as building block methodology, efficient sampling of distributions on the sphere is highly appreciated. We propose a shrinkage based and an idealized geodesic slice sampling Markov chain, designed to generate approximate samples from distributions on the sphere. In particular, the shrinkage based algorithm works in any dimension, is straight-forward to implement and has no algorithmic parameters such that no tuning is necessary. Apart from the verification of reversibility we show under weak regularity conditions on the target distribution that geodesic slice sampling is uniformly geometrically ergodic, i.e., uniform exponential convergence to the target is proven.

翻译：受球体限制的概率措施构成一个重要的统计模型类别,并用于模拟方向数据或形状等。因此,作为构件方法,对球体分布的高效取样受到高度赞赏。我们建议采用基于缩缩和理想化的大地切片取样马可夫链,目的是从球体分布中产生大致的样本。特别是,基于缩缩缩算法在任何层面都起作用,可以直接向前推进实施,而且没有无需调整的算法参数。除了在目标分布的薄弱常规条件下核实可逆性外,我们还证明,大地切片取样具有统一的几何分率,即与目标的统一指数趋同得到证明。