论文标题
泊松高斯混合物过程：非高斯地统计建模的灵活而强大的方法
The Poisson-Gaussian Mixture Process: A Flexible and Robust Approach for Non-Gaussian Geostatistical Modeling
论文作者
论文摘要
本文介绍了一个新型的地统计模型系列，旨在捕获传统高斯流程超出范围的复杂特征。拟议中的家族称为泊松 - 高斯混合物过程（POGAMP），是在层次上指定的，将高斯过程的无限二维动力学与任何多元连续分布相结合。这种组合是由潜在的泊松过程随机定义的，允许Pogamp定义具有有限维分布的有效过程，可以近似任何连续分布。与其他非高斯地统计模型不同，这些模型可能无法通过分配任意的有限维分布来确保过程的有效性，而Pogamp保留了对于建模和推理至关重要的基本概率特性。我们建立了有关Pogamp的存在和特性的正式结果，突出了其在捕获复杂空间模式时的稳健性和灵活性。为了支持实际应用，当在某些空间域中离散地观察到Pogamp时，为贝叶斯推断开发了精心设计的MCMC算法。
This paper introduces a novel family of geostatistical models designed to capture complex features beyond the reach of traditional Gaussian processes. The proposed family, termed the Poisson-Gaussian Mixture Process (POGAMP), is hierarchically specified, combining the infinite-dimensional dynamics of Gaussian processes with any multivariate continuous distribution. This combination is stochastically defined by a latent Poisson process, allowing the POGAMP to define valid processes with finite-dimensional distributions that can approximate any continuous distribution. Unlike other non-Gaussian geostatistical models that may fail to ensure validity of the processes by assigning arbitrary finite-dimensional distributions, the POGAMP preserves essential probabilistic properties crucial for both modeling and inference. We establish formal results regarding the existence and properties of the POGAMP, highlighting its robustness and flexibility in capturing complex spatial patterns. To support practical applications, a carefully designed MCMC algorithm is developed for Bayesian inference when the POGAMP is discretely observed over some spatial domain.
