The paper considers a Cox process where the stochastic intensity function for the Poisson data model is itself a non-homogeneous Poisson process. We show that it is possible to obtain the marginal data process, namely a non-homogeneous count process exhibiting over-dispersion. While the intensity function is non-decreasing, it is straightforward to transform the data so that a non-decreasing intensity function is appropriate. We focus on a time series for arrival times of a process and, in particular, we are able to find an exact form for the marginal probability for the observed data, so allowing for an easy to implement estimation algorithm via direct calculations of the likelihood function.

翻译：本文考虑一类Cox过程，其中泊松数据模型的随机强度函数本身是一个非齐次泊松过程。我们证明可以获取边缘数据过程，即表现为过离散的非齐次计数过程。由于强度函数非递减，可通过数据变换使其适用于非递减强度函数情形。我们聚焦于过程到达时间的时间序列分析，特别地，能够推导出观测数据边缘概率的精确表达式，从而通过直接计算似然函数实现简便的估计算法。