Spatial Point Pattern Analysis Using Composite Likelihood

利用复合似然的思想，提出了一种新的基于似然的空间点过程模型拟合方法。合成似然(CL)已被成功地应用于许多完全最大似然不可行或不可用的环境中。然而，它在空间点过程建模中的应用却从未被研究过。这项研究的目的是证明，对于任何一个可以显式定义二阶强度函数的空间点过程，都可以形成一个CL。所提出的似然比易于获得，并可用于许多不同的空间点模式分析。特别是，它可以用来对均匀和非均匀空间点过程模型进行数据拟合。此外，它还可以用来选择用于估计对相关函数的带宽，这是空间点格局分析中一个非常探索性和模型拟合的工具。这项研究是由阿肯色大学昆虫学家收集的红栎虫数据推动的。这些数据包括红橡树钻孔虫幼虫在进食树木时造成的攻击洞的地图位置。主要目的是了解是什么影响成年红橡树钻孔虫决定在哪里产卵。建议的模型拟合程序将用于将攻击孔的位置与重要的树木特征联系起来，例如树木的侧面和高度。这项工作具有重要的生物学意义和现实意义。特别是，这些结果将为了解成虫的繁殖习性提供生物学上的见解。反过来，这种生物学上的洞察力可以用来指导开发更有效的诱捕技术，这些技术可以用来控制红栎虫的数量。因此，这项拟议的研究可能会在拯救美国数百万棵正受到红栎虫爆发威胁的红橡树的努力中发挥关键作用。

The proposed research introduces a new likelihood based method in fitting spatial point process models using the idea of composite likelihood. Composite likelihood (CL) has been successfully applied in numerous settings where a full maximum likelihood is not feasible or is not available. Its use in spatial point process modeling, however, has never been studied. This research intends to show that a CL can be formed for any spatial point process whose second-order intensity function can be explicitly defined. The proposed likelihood is easy to obtain and can be used in many different spatial point pattern analyses. In particular, it can be used to fit both homogeneous and inhomogeneous spatial point process models to data. Furthermore, it can also be used to select the bandwidth used in estimating the pair correlation function, which is an extremely exploratory and model fitting tool in spatial point pattern analysis.This research is motivated by the red oak borer data that were collected by entomologists at the University of Arkansas. The data consist of mapped locations of attack holes caused by larvae of red oak borers when they eat their way into the trees. The main objective is to understand what affects adult red oak borers to decide where to lay their eggs. The proposed model fitting procedures will be applied to link the locations of attack holes to important tree characteristics such as side and height of the tree. This work will have both important biological and practical significance. In particular, the results will provide biological insight on the breeding habit of the adult borers. This biological insight can in turn be used in practice to guide the development of more effective trapping techniques that can be used to control the population of the red oak borers. Thus the proposed research may play a critical role in the effort to save millions of red oak trees in the US that are being threatened by the outbreaks of red oak borers.