Cox processes are natural models for point process phenomena that are environmentally driven, but much less natural for phenomena driven primarily by interactions amongst the points. The class of log-Gaussian Cox processes (LGCPs) has an elegant simplicity, and one of its attractive features is the tractability of the multivariate normal distribution carries over, to some extent, to the associated Cox process. In the statistical analysis of spatial point patterns, it is often assumed isotropy because of a simpler interpretation and ease of analysis. However, there are many cases in which the spatial structure depends on the direction. In this paper, we introduce new families of anisotropic spatial LGCPs that are useful to model spatial anisotropic point patterns that exhibit a degree of clustering. We propose classes of families consisting of elliptical and non-elliptical models. The former can be reduced to isotropic forms after some rotations, while the latter family goes beyond this property. We derive analytical forms for the covariance of the associated random field, and some second-order characteristics. A moment-based estimation procedure is followed to make inference on the parameters that control the degree of anisotropy. The estimation procedure is evaluated through a simulation study under a variety of scenarios and various degrees of anisotropy. Our methodology is illustrated on two real datasets of earthquakes in South America and the Mediterranean Europe.

Cox过程是环境驱动的点过程现象的自然模型，但是对于主要由点之间的交互作用引起的现象而言，Cox过程自然而然。对数高斯Cox过程（LGCP）具有优雅的简单性，其吸引人的特征之一是多元正态分布的可处理性在一定程度上延续了相关的Cox过程。在空间点模式的统计分析中，由于解释更简单且易于分析，通常将其假定为各向同性。但是，在许多情况下，空间结构取决于方向。在本文中，我们介绍了各向异性空间LGCP的新族，这些族对建模具有一定聚集度的空间各向异性点模式很有用。我们提出了由椭圆和非椭圆模型组成的家庭类别。旋转一些后，前者可以还原为各向同性形式，而后者家族则超越了这一性质。我们推导了相关随机场的协方差和一些二阶特征的解析形式。遵循基于矩的估计程序以推断控制各向异性程度的参数。通过在各种情况和不同程度的各向异性下进行的仿真研究来评估估计程序。我们的方法论在南美和地中海欧洲的两个真实地震数据集上得到了说明。我们推导了相关随机场的协方差和一些二阶特征的解析形式。遵循基于矩的估计程序以推断控制各向异性程度的参数。通过在各种情况和不同程度的各向异性下进行的仿真研究来评估估计程序。我们的方法论在南美和地中海欧洲的两个真实地震数据集上得到了说明。我们推导了相关随机场的协方差和一些二阶特征的解析形式。遵循基于矩的估计程序以推断控制各向异性程度的参数。通过在各种情况和不同程度的各向异性下进行的仿真研究来评估估计程序。我们的方法论在南美和地中海欧洲的两个真实地震数据集上得到了说明。