空间点模式统计学的一些最新进展
Some recent developments in statistics for spatial point patterns
摘要：
本文回顾了在过去十年中获得的空间点过程统计的发展。这些发展包括新的类的空间点过程模型，如行列式点过程，模型结合了规律性和聚集，模型点随机分布在潜在的几何结构。关于参数推断的主要重点是各种类型的估计功能来自所谓的创新措施。这种估计函数的最优性进行了讨论，以及计算问题。还简要地讨论了定点过程的极大似然推断和贝叶斯推断。关于非参数推理，我们认为扩展功能汇总统计量的情况下，非齐次点过程以及新的方法，以模拟为基础的推理。
英文摘要：
This paper reviews developments in statistics for spatial point processes obtained within roughly the last decade. These developments include new classes of spatial point process models such as determinantal point processes, models incorporating both regularity and aggregation, and models where points are randomly distributed around latent geometric structures. Regarding parametric inference the main focus is on various types of estimating functions derived from so-called innovation measures. Optimality of such estimating functions is discussed as well as computational issues. Maximum likelihood inference for determinantal point processes and Bayesian inference are briefly considered too. Concerning non-parametric inference, we consider extensions of functional summary statistics to the case of inhomogeneous point processes as well as new approaches to simulation based inference.
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