The performance of Markov chain Monte Carlo samplers strongly depends on the properties of the target distribution such as its covariance structure, the location of its probability mass and its tail behavior. We explore the use of bijective affine transformations of the sample space to improve the properties of the target distribution and thereby the performance of samplers running in the transformed space. In particular, we propose a flexible and user-friendly scheme for adaptively learning the affine transformation during sampling. Moreover, the combination of our scheme with Gibbsian polar slice sampling is shown to produce samples of high quality at comparatively low computational cost in several settings based on real-world data.

翻译：马尔可夫链蒙特卡洛采样器的性能在很大程度上取决于目标分布的特性，如其协方差结构、概率质量的位置以及尾部行为。本文探讨了使用样本空间的双射仿射变换来改善目标分布的特性，从而提升在变换空间中运行的采样器的性能。特别地，我们提出了一种灵活且用户友好的方案，用于在采样过程中自适应地学习仿射变换。此外，在多个基于真实数据的场景中，我们的方案与吉布斯极坐标切片采样相结合，被证明能以相对较低的计算成本生成高质量的样本。