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Bayesian inference for Gaussian excursion set generated Cox processes with set-marking

机译：高斯偏移集的贝叶斯推断生成带有集标记的Cox过程

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摘要

This work considers spatial Cox point processes where the random intensity is defined by a random closed set such that different point intensities appear in the two phases formed by the random set and its complement. The point pattern is observed as a set of point coordinates in a bounded region W(C)R~d together with the information on the phase of the location of each point. This phase information, called set-marking, is not a representative sample from the random set, and hence it cannot be directly used for deducing properties of the random set. Excursion sets of continuous-parameter Gaussian random fields are applied as a flexible model for the random set. Fully Bayesian method and Markov chain Monte Carlo (MCMC) simulation is adopted for inferring the parameters of the model and estimating the random set. The performance of the new approach is studied by means of simulation experiments. Further, two forestry data sets on point patterns of saplings are analysed. The saplings grow in a clear-cut forest area where, before planting and natural seeding, the soil has been mounded forming a blotched soil structure. The tree densities tend to be different in the tilled patches and in the area outside the patches. The coordinates of each sapling have been measured and it is known whether this location is in a patch or outside. This example has been a motivation for the study.
机译：这项工作考虑了空间Cox点过程，其中随机强度是由随机封闭集定义的，从而在随机集及其补集形成的两个阶段中会出现不同的点强度。观察点图案作为边界区域W（C）R_d中的一组点坐标以及关于每个点的位置的相位的信息。此相位信息称为集合标记，它不是随机集合的代表样本，因此不能直接用于推导随机集合的属性。连续参数高斯随机场的偏移集被用作该随机集的灵活模型。采用全贝叶斯方法和马尔可夫链蒙特卡洛（MCMC）仿真来推断模型的参数并估计随机集。通过仿真实验研究了新方法的性能。此外，分析了关于树苗点型的两个林业数据集。幼树生长在一个开阔的森林地区，在播种和自然播种之前，这里的土壤已被堆成土，形成了斑点的土壤结构。在耕作的斑块中和斑块外部的区域中，树木密度趋于不同。已测量每个树苗的坐标，并且知道该位置是在补丁中还是在外部。这个例子是本研究的动机。

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