We propose models and algorithms for learning about random directions in simplex-valued data. The models are applied to the study of income level proportions and their changes over time in a geostatistical area. There are several notable challenges in the analysis of simplex-valued data: the measurements must respect the simplex constraint and the changes exhibit spatiotemporal smoothness and may be heterogeneous. To that end, we propose Bayesian models that draw from and expand upon building blocks in circular and spatial statistics by exploiting a suitable transformation for the simplex-valued data. Our models also account for spatial correlation across locations in the simplex and the heterogeneous patterns via mixture modeling. We describe some properties of the models and model fitting via MCMC techniques. Our models and methods are applied to an analysis of movements and trends of income categories using the Home Mortgage Disclosure Act data.

翻译：本文提出针对单形数据中随机方向进行学习的模型与算法。该模型应用于地理统计区域中收入水平比例及其随时间变化的研究。分析单形数据面临若干显著挑战：测量值须满足单形约束，其变化呈现时空平滑性且可能存在异质性。为此，我们通过利用适用于单形数据的变换方法，借鉴并扩展了圆形统计与空间统计的基本框架，提出了贝叶斯模型。本模型还通过混合建模方法，考虑了单形内不同位置间的空间相关性及异质性模式。我们描述了模型的若干特性，并采用MCMC技术进行模型拟合。最终将所提模型与方法应用于家庭抵押贷款披露法案数据中的收入类别移动趋势分析。