Dirichlet processes and their extensions have reached a great popularity in Bayesian nonparametric statistics. They have also been introduced for spatial and spatio-temporal data, as a tool to analyze and predict surfaces. A popular approach to Dirichlet processes in a spatial setting relies on a stick-breaking representation of the process, where the dependence over space is described in the definition of the stick-breaking probabilities. Extensions to include temporal dependence are still limited, however it is important, in particular for those phenomena which may change rapidly over time and space, with many local changes. In this work, we propose a Dirichlet process where the stick-breaking probabilities are defined to incorporate both spatial and temporal dependence. We will show that this approach is not a simple extension of available methodologies and can outperform available approaches in terms of prediction accuracy. An advantage of the method is that it offers a natural way to test for separability of the two components in the definition of the stick-breaking probabilities.

翻译：狄利克雷过程及其扩展在贝叶斯非参数统计中获得了广泛的应用。它们也被引入到空间和时空数据领域，作为分析和预测曲面的一种工具。在空间设定下，狄利克雷过程的一种流行方法依赖于过程的stick-breaking表示，其中空间依赖性通过stick-breaking概率的定义来描述。然而，包含时间依赖性的扩展仍然有限，但对于那些可能在时间和空间上快速变化、存在大量局部变化的现像尤为重要。在本研究中，我们提出一种狄利克雷过程，其stick-breaking概率的定义同时融合了空间和时间依赖性。我们将证明，该方法并非现有技术的简单扩展，并且在预测精度上能够超越已有的方法。该方法的一个优势在于，它提供了一种自然的方式来检验stick-breaking概率定义中两个组分的可分性。