Point Pattern Analysis of Tropical Tree Populations Developing Flexible Spatial Models with Complex Boundary Structures

估计物种分布、种群数量和栖息地关系的生态模型往往依赖于在应用领域不现实的统计假设。标准点过程模型尤其依赖于完美可检测性和独立性的假设，而这些假设不太可能成立。这些假设可以通过结合用于检测的模型和用于解释未观察到的异质性原因的结构化随机效应的模型来放松。目前的现状通常涉及两阶段方法，分别拟合空间模型的可检测性和结构随机效应的样条法。该PHD建立在近似贝叶斯推理(集成嵌套拉普拉斯近似)和高斯马尔可夫随机场(GMRF)近似的最新发展的基础上，建立了同时考虑未观察到的异质性和检测过程的1阶段点过程模型。还可以将GMRF的发展纳入生态应用中常见的其他类型的空间模型，如空间捕获-再捕获模型，这些模型具有类似的独立性假设，但在实践中很难满足这些假设。

Ecological models to estimate species distributions, population size and habitat associations often rely on statistical assumptions that are unrealistic in the domain of application. Standard point process models in particular rely on assumptions of perfect detectability and independence that are unlikely to hold. These assumptions can be relaxed by incorporating models for detection and for structured random effects that account for unobserved causes of heterogeneity. The current status quo often involves a 2-stage approach, fitting detectability separately from spatial models and a spline approach for the structured random effect.This PhD builds on recent developments in approximate Bayesian inference (Integrated Nested Laplace Approximation) and the approximation of Gaussian Markov random fields (GMRF) to develop 1-stage point process models that simultaneously account for unobserved heterogeneity and the detection process. There is also scope to include the GMRF developments in other types of spatial models common in ecological applications such as spatial capture-recapture models, which share similar assumptions about independence that are hard to meet in practice.