This paper introduces a new approach to inferring the second order properties of a multivariate log Gaussian Cox process (LGCP) with a complex intensity function. We assume a semi-parametric model for the multivariate intensity function containing an unspecified complex factor common to all types of points. Given this model we exploit the availability of several types of points to construct a second-order conditional composite likelihood to infer the pair correlation and cross pair correlation functions of the LGCP. Crucially this likelihood does not depend on the unspecified part of the intensity function. We also introduce a cross validation method for model selection and an algorithm for regularized inference that can be used to obtain sparse models for cross pair correlation functions. The methodology is applied to simulated data as well as data examples from microscopy and criminology. This shows how the new approach outperforms existing alternatives where the intensity functions are estimated non-parametrically.
翻译:本文引入了一种新的方法来推断具有复杂强度函数的多变量日志 Gausian Cox 进程(LGCP) 的第二顺序属性。 我们假设了多变量强度函数的半参数模型, 包含所有类型点共有的未具体说明的复杂因素。 根据这个模型, 我们利用多种类型的点来构建一个第二顺序有条件的复合可能性, 以推断 LGCP 的对对相关和对对相关功能。 关键是, 这种可能性并不取决于强度函数中未指明的部分。 我们还引入了用于模型选择的交叉验证方法, 以及可用于获取交叉关联函数的稀有模型的逻辑推算法。 该方法用于模拟数据以及微生物和犯罪学的数据示例。 这显示了新方法如何在强度函数是非参数估计的情况下超越现有替代品。