Cluster point processes comprise a class of models that have been used for a wide range of applications. While several models have been studied for the probability density function of the offspring displacements and the parent point process, there are few examples of non-Poisson distributed cluster sizes. In this paper, we introduce a generalization of the Thomas process, which allows for the cluster sizes to have a variance that is greater or less than the expected value. We refer to this as the cluster sizes being over- and under-dispersed, respectively. To fit the model, we introduce minimum contrast methods and a Bayesian MCMC algorithm. These are evaluated in a simulation study. It is found that using the Bayesian MCMC method, we are in most cases able to detect over- and under-dispersion in the cluster sizes. We use the MCMC method to fit the model to nerve fiber data, and contrast the results to those of a fitted Thomas process.

聚类点过程包括一类已被广泛应用的模型。虽然已经研究了几种模型来分析后代位移和母点过程的概率密度函数，但很少有非泊松分布簇大小的示例。在本文中，我们介绍了托马斯过程的一般化，该过程允许群集大小的方差大于或小于预期值。我们将其称为簇大小分别过度分散和分散不足。为了拟合模型，我们引入了最小对比度方法和贝叶斯MCMC算法。这些在模拟研究中进行评估。发现使用贝叶斯MCMC方法，在大多数情况下，我们能够检测出簇大小的过度分散和分散不足。