基于数据增强的Sigmoidal高斯Cox过程贝叶斯分析
Bayesian Analysis of Sigmoidal Gaussian Cox Processes via Data Augmentation
AI总结：
本文回归点过程分布理论基础，建立稀疏机制与点联合密度的联系，用数据增强解决边缘模型难解问题，修正sigmoidal高斯Cox过程推断的矛盾，还提出多类型扩展并在树种数据上验证了带不确定性量化的类型间依赖建模效果。
摘要：
许多点过程数据模型通过稀疏（thinning）过程定义：基础过程（通常为Poisson过程）的点要么被保留（观测到），要么被丢弃（被稀疏）。本文回归点过程分布理论的基础，建立了基础稀疏机制与这类模型中被稀疏点和观测点联合密度之间的联系。实践中，观测点的边缘模型通常难以处理，但可以从条件分布中采样得到被稀疏点的实例，并采用典型的数据增强方案来规避这一问题。这类方法在近期文献中已有应用，但不同出版物之间存在一些不一致之处。我们聚焦于一个例子：所谓的sigmoidal高斯Cox过程。我们应用所提方法解决了该模型推断过程中数据增强步骤里相互矛盾的观点。我们还对该过程进行了多类型扩展，并对密歇根州Lansing Woods中两种不同树种的位置数据进行贝叶斯推断，研究重点是带贝叶斯不确定性量化的类型间依赖建模。
英文摘要：
Many models for point process data are defined through a thinning procedure where locations of a base process (often Poisson) are either kept (observed) or discarded (thinned). In this paper, we go back to the fundamentals of the distribution theory for point processes to establish a link between the base thinning mechanism and the joint density of thinned and observed locations in any of such models. In practice, the marginal model of observed points is often intractable, but thinned locations can be instantiated from their conditional distribution and typical data augmentation schemes can be employed to circumvent this problem. Such approaches have been employed in the recent literature, but some inconsistencies have been introduced across the different publications. We concentrate on an example: the so-called sigmoidal Gaussian Cox process. We apply our approach to resolve contradicting viewpoints in the data augmentation step of the inference procedures therein. We also provide a multitype extension to this process and conduct Bayesian inference on data consisting of positions of two different species of trees in Lansing Woods, Michigan. The emphasis is put on intertype dependence modeling with Bayesian uncertainty quantification.
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