This paper presents a spatial process with covariate-dependent random joint distributions. Our construction is based on an extension of the Gaussian copula model using the Beta-regression process. As a generalized form of stick-breaking processes, the proposed model allows the covariance function to be covariate-driven nonstationary. Also, the resulting labeling process provides a covariate-dependent random partitioning. Markov chain Monte Carlo methods are used to make Bayesian inferences. The effectiveness of this model in segmentation of the domain and prediction performance are assessed through a simulation study. Additionally, results from a real dataset demonstrate that the proposed model possesses better spatial prediction performance over other competing models.

本文提出了一个与协变量相关的随机联合分布的空间过程。我们的构造基于使用 Beta 回归过程的高斯 copula 模型的扩展。作为一种广义的断棒过程，所提出的模型允许协方差函数是协变量驱动的非平稳的。此外，由此产生的标记过程提供了一个依赖于协变量的随机分区。马尔可夫链蒙特卡罗方法用于进行贝叶斯推理。通过模拟研究评估了该模型在域分割和预测性能方面的有效性。此外，来自真实数据集的结果表明，所提出的模型比其他竞争模型具有更好的空间预测性能。