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Inference for cluster point processes with over- or under-dispersed cluster sizes

机译：对具有超出或欠分散的簇大小的集群点进程的推断

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摘要

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.
机译：群集点流程包括一类用于广泛应用的模型。虽然已经研究了几种模型的后代位移和父点过程的概率密度函数，但是少数非泊松分布式簇大小的例子。在本文中，我们介绍了托马斯过程的概括，这允许群集大小具有更大或小于预期值的方差。我们将此指代，因为群集尺寸分别超过和欠分散。为了适应模型，我们介绍了最小的对比度方法和贝叶斯MCMC算法。这些是在模拟研究中进行评估的。有人发现，使用贝叶斯MCMC方法，我们在大多数情况下都能够检测群集大小的过度和分散。我们使用MCMC方法将模型拟合到神经光纤数据，并将结果对比托马斯过程的结果。

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