The theoretical foundation for a number of model selection criteria is established in the context of inhomogeneous point processes and under various asymptotic settings: infill, increasing domain and combinations of these. For inhomogeneous Poisson processes we consider Akaike's information criterion and the Bayesian information criterion, and in particular we identify the point process analogue of ‘sample size’ needed for the Bayesian information criterion. Considering general inhomogeneous point processes we derive new composite likelihood and composite Bayesian information criteria for selecting a regression model for the intensity function. The proposed model selection criteria are evaluated using simulations of Poisson processes and cluster point processes.

中文翻译：

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非均匀空间点过程的信息标准

许多模型选择标准的理论基础是在非均匀点过程的背景下和各种渐近设置下建立的：填充、增加域和这些的组合。对于非齐次泊松过程，我们考虑 Akaike 的信息准则和贝叶斯信息准则，特别是我们确定了贝叶斯信息准则所需的“样本大小”的点过程模拟。考虑到一般的非齐次点过程，我们推导出新的复合似然和复合贝叶斯信息标准，用于选择强度函数的回归模型。使用泊松过程和聚类点过程的模拟来评估建议的模型选择标准。