Bayesian mixture modeling for spatial Poisson process intensities, with applications to extreme value analysis
Bayesian mixture modeling for spatial Poisson process intensities, with applications to extreme value analysis
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DOI：
10.1016/j.jspi.2006.05.022
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发表时间：
2007-10-01
影响因子：
0.9
通讯作者：
Sanso, Bruno
中科院分区：
文献类型：
--
作者：
Kottas, Athanasios;Sanso, Bruno
我们提出了一种方法来分析的空间点模式，这是假设出现作为一组观察从一个空间非齐次泊松过程。在有界区域中观察到空间点模式，对于大多数应用，该区域被认为是定义过程的空间中的矩形。该方法是基于建模的密度函数，定义在这个有界区域，这是直接相关的强度函数的泊松过程。我们开发了一个灵活的非参数混合模型，这个密度使用一个二元Beta分布的混合内核和Dirichlet过程之前的混合分布。使用后验模拟方法，我们得到完整的推理的强度函数和任何其他功能的过程中，可能感兴趣的。我们讨论的应用程序的空间点模式的聚类推理的问题是感兴趣的。此外，我们考虑应用的方法，极值分析问题。我们用三个以前发表的数据集来说明建模方法。其中两个数据集来自林业，包括树木的位置。第三个数据集包括道琼斯指数在1303天内的极端情况。(C)2007 Elsevier B.V.保留所有权利。
We propose a method for the analysis of a spatial point pattern, which is assumed to arise as a set of observations from a spatial nonhomogeneous Poisson process. The spatial point pattern is observed in a bounded region, which, for most applications, is taken to be a rectangle in the space where the process is defined. The method is based on modeling a density function, defined on this bounded region, that is directly related with the intensity function of the Poisson process. We develop a flexible nonparametric mixture model for this density using a bivariate Beta distribution for the mixture kernel and a Dirichlet process prior for the mixing distribution. Using posterior simulation methods, we obtain full inference for the intensity function and any other functional of the process that might be of interest. We discuss applications to problems where inference for clustering in the spatial point pattern is of interest. Moreover, we consider applications of the methodology to extreme value analysis problems. We illustrate the modeling approach with three previously published data sets. Two of the data sets are from forestry and consist of locations of trees. The third data set consists of extremes from the Dow Jones index over a period of 1303 days. (C) 2007 Elsevier B.V. All rights reserved.