Spatial Point Pattern Analysis Using Composite Likelihood

提出了一种新的基于似然的空间点过程模型拟合方法，利用复合似然的思想。复合似然（CL）已成功地应用于许多情况下，一个完整的最大似然是不可行的或不可用。然而，它在空间点过程建模中的应用从未被研究过。这项研究旨在表明，任何二阶强度函数可以明确定义的空间点过程都可以形成CL。建议的似然是很容易获得，并可用于许多不同的空间点模式分析。特别是，它可以用来拟合均匀和非均匀的空间点过程模型的数据。此外，它还可以用来选择用于估计对相关函数的带宽，这是一个非常具有探索性和模型拟合的工具在空间点格局分析。本研究的动机是由昆虫学家在阿肯色州收集的红橡树螟数据。这些数据包括红橡树蛀虫幼虫啃食树木时造成的攻击孔的地图位置。主要目的是了解是什么影响了成年红橡木蛀虫决定在哪里产卵。建议的模型拟合程序将被应用于连接的攻击孔的位置，重要的树木特征，如树木的侧面和高度。这项工作将具有重要的生物学意义和实际意义。特别是，这些结果将提供生物学上的洞察成虫的繁殖习性。这种生物学上的见解反过来可以在实践中用于指导更有效的诱捕技术的发展，这些技术可以用于控制红橡树钻蛀者的数量。因此，拟议的研究可能在拯救美国数百万棵受到红橡树蛀虫爆发威胁的红橡树方面发挥关键作用。

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.