论文标题
贝叶斯分析Sigmoidal Gaussian Cox过程通过数据增强
Bayesian Analysis of Sigmoidal Gaussian Cox Processes via Data Augmentation
论文作者
论文摘要
许多用于点过程数据的模型是通过稀疏过程定义的，在稀疏过程中，基本过程的位置（通常是泊松）要么保存（观察到）或丢弃（稀释）。在本文中，我们回到了分布理论的基础上，以在任何此类模型中建立基础稀疏机制与稀薄和观察到的位置的关节密度之间建立联系。在实践中，观察到的点的边际模型通常是棘手的，但是可以从其条件分布中实例化的位置，并且可以采用典型的数据增强方案来解决此问题。这种方法已在最近的文献中采用，但是在不同的出版物中引入了一些不一致之处。我们集中在一个例子上：所谓的Sigmoidal Gaussian Cox过程。我们采用我们的方法来解决其中推理程序的数据扩展步骤中的矛盾观点。我们还为此过程提供了多个扩展，并对密歇根州兰斯林中的两种不同树木的位置组成的数据进行了贝叶斯推断。重点是与贝叶斯不确定性定量的类型依赖性建模。
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.
