Neyman-Scott processes (NSPs) are point process models that generate clusters of points in time or space. They are natural models for a wide range of phenomena, ranging from neural spike trains to document streams. The clustering property is achieved via a doubly stochastic formulation: first, a set of latent events is drawn from a Poisson process; then, each latent event generates a set of observed data points according to another Poisson process. This construction is similar to Bayesian nonparametric mixture models like the Dirichlet process mixture model (DPMM) in that the number of latent events (i.e. clusters) is a random variable, but the point process formulation makes the NSP especially well suited to modeling spatiotemporal data. While many specialized algorithms have been developed for DPMMs, comparatively fewer works have focused on inference in NSPs. Here, we present novel connections between NSPs and DPMMs, with the key link being a third class of Bayesian mixture models called mixture of finite mixture models (MFMMs). Leveraging this connection, we adapt the standard collapsed Gibbs sampling algorithm for DPMMs to enable scalable Bayesian inference on NSP models. We demonstrate the potential of Neyman-Scott processes on a variety of applications including sequence detection in neural spike trains and event detection in document streams.

翻译：奈曼-斯科特过程（NSP）是一类生成时间或空间点簇的点过程模型。这类模型是神经脉冲序列到文档流等多种自然现象的经典建模工具。其聚类特性通过双随机机制实现：首先从泊松过程中抽取一组潜在事件，随后每个潜在事件依据另一个泊松过程生成一组观测数据点。该构建方式类似于狄利克雷过程混合模型（DPMM）等贝叶斯非参数混合模型——潜在事件（即聚类）数量同为随机变量，但点过程的数学表述使NSP特别适用于时空数据建模。尽管DPMM已发展出众多专用算法，但针对NSP推断的研究相对较少。本文揭示了NSP与DPMM之间的创新性关联，其关键衔接点在于第三类贝叶斯混合模型——有限混合混合模型（MFMM）。借助该关联，我们将DPMM的标准折叠吉布斯采样算法适配至NSP模型，实现可扩展的贝叶斯推断。通过在神经脉冲序列中的序列检测与文档流中的事件检测等多类应用中，验证了奈曼-斯科特过程的潜力。