We propose a hierarchical log Gaussian Cox process (LGCP) for point patterns, where a set of points \(\varvec{x}\) affects another set of points \(\varvec{y}\) but not vice versa. We use the model to investigate the effect of large trees on the locations of seedlings. In the model, every point in \(\varvec{x}\) has a parametric influence kernel or signal, which together form an influence field. Conditionally on the parameters, the influence field acts as a spatial covariate in the intensity of the model, and the intensity itself is a non-linear function of the parameters. Points outside the observation window may affect the influence field inside the window. We propose an edge correction to account for this missing data. The parameters of the model are estimated in a Bayesian framework using Markov chain Monte Carlo where a Laplace approximation is used for the Gaussian field of the LGCP model. The proposed model is used to analyze the effect of large trees on the success of regeneration in uneven-aged forest stands in Finland.

我们为点模式提出了一个分层对数高斯考克斯过程（LGCP），其中一组点\(\varvec{x}\)影响另一组点\(\varvec{y}\)但反之则不然。我们使用该模型来研究大树对幼苗位置的影响。在模型中，\(\varvec{x}\) 中的每个点具有参数化影响核或信号，它们共同形成影响场。以参数为条件，影响场作为模型强度的空间协变量，强度本身是参数的非线性函数。观察窗外的点可能会影响窗内的影响场。我们建议进行边缘校正以解决此缺失数据。该模型的参数是在贝叶斯框架中使用马尔可夫链蒙特卡罗来估计的，其中拉普拉斯近似用于 LGCP 模型的高斯场。所提出的模型用于分析大树对芬兰不均匀林分更新成功的影响。