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

估计物种分布、种群规模和栖息地关联的生态模型往往依赖于在应用领域不切实际的统计假设。特别是标准点过程模型依赖于不太可能成立的完美可检测性和独立性的假设。这些假设可以通过合并检测模型和结构化随机效应模型来放松，这些模型解释了未观察到的异质性原因。目前的现状往往涉及2阶段的方法，拟合检测能力分别从空间模型和样条方法的结构化random effects.This博士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）的近似的最新发展，开发1阶段点过程模型，同时考虑未观察到的异质性和检测过程。也有范围，包括其他类型的空间模型，如空间捕获-再捕获模型，共享类似的假设，在实践中很难满足的独立性，在生态应用中常见的GMRF的发展。

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.