Functional summary statistics for point processes on the sphere with an application to determinantal point processes
Functional summary statistics for point processes on the sphere with an application to determinantal point processes
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DOI：
10.1016/j.spasta.2016.06.004
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发表时间：
2016-11-01
影响因子：
2.3
通讯作者：
Rubak, Ege
中科院分区：
文献类型：
--
作者：
Moller, Jesper;Rubak, Ege
我们研究了d维单位球面S-d上的点过程，考虑了各向同性和各向异性的情形，主要集中在d = 2的球面情形.第一部分研究约化Palm分布和函数汇总统计量，包括最近邻函数、空空间函数、Ripley函数和非齐次K函数。第二部分讨论了球面上决定点过程模型的吸引力性质，并考虑了函数汇总统计量在决定点过程中的应用。事实上，DPPs表现出排斥性，但我们也使用它们与某些相关的细化时，构建点过程模型的大规模聚集和小规模的规则性。最后，我们讨论了未来的工作统计空间点过程的领域。(C)2016爱思唯尔B. V.保留所有权利。
We study point processes on Sd, the d-dimensional unit sphere S-d, considering both the isotropic and the anisotropic case, and focusing mostly on the spherical case d = 2. The first part studies reduced Palm distributions and functional summary statistics, including nearest neighbour functions, empty space functions, and Ripley's and inhomogeneous K-functions. The second part partly discusses the appealing properties of determinantal point process (DPP) models on the sphere and partly considers the application of functional summary statistics to DPPs. In fact DPPs exhibit repulsiveness, but we also use them together with certain dependent thinnings when constructing point process models on the sphere with aggregation on the large scale and regularity on the small scale. We conclude with a discussion on future work on statistics for spatial point processes on the sphere. (C) 2016 Elsevier B.V. All rights reserved.