The development of statistical methodology and computational techniques for the modelling of complex ecological data

这项研究计划的中心是开发显示空间和/或数据的统计方法 时间上的依赖关系，对什么对生态重要有特别的兴趣。 状态空间模型(SSM)正在成为分析动物跟踪数据的标准工具，但它的计算量很大，很难实现，特别是在涉及参数估计的时候。提出了在MatLab中使用粒子滤波方法来实现SSMS跟踪数据，从而a)极大地促进了复杂环境数据的集成，b)实现了在线拟合，c)允许通过状态增广来估计时变参数。到那时，生态学家将更容易接触到SSMS，从而有可能提出关于动物如何与环境相关的重要问题。 广义加性模型(GAM)正在成为分析生态数据的非常流行的工具，但它对偏离假设模型的观测值的存在非常敏感。首先，将对R中两种流行的适合GAM的方法(MGCv和GAM)进行正式比较，并特别注意与稳健性和生态数据有关的问题。然后对mgcv进行改进，以便为模型参数提供稳健的点估计，以及稳健地获得平滑参数。还将开发一种计算参数的置信度区间的新方法，该方法避免了在MGCV内可用的贝叶斯方法。最后，将探讨包括一致性在内的问题，以努力使更好的工具可用于执行模型选择。 带有多余零的聚集计数数据是关于濒危物种，特别是在海洋环境中收集的那种数据的典型。将开发随机效应障碍模型，允许模型每个部分的协变量集可能重叠，并预测特定于集群的目标。这些模型将使生态学家能够回答与预期丰度相关的关键问题。

This research proposal centers on the development of statistical methodology for data exhibiting spatial and/or temporal dependencies with a particular interest in what is important for ecology. State-space models (SSMs) are becoming standard tools for the analysis of animal tracking data and yet can be computationally intensive and difficult to implement, particularly when parameter estimation is involved. Particle Filter methods in MATLAB are proposed to implement SSMs for tracking data thereby a) greatly facilitating the integration of complex environmental data, b) enabling online fitting and c) allowing estimation of time-varying parameters via state augmentation. SSMs will then be far more accessible to ecologists, making it possible to ask important questions about how animals move in relation to their environment. Generalized Additive Models (GAMs) are becoming very popular tools for analyzing ecological data and yet can be very sensitive to the presence of observations that deviate from the assumed model. First a formal comparison of the two popular approaches for fitting GAMs in R (mgcv and gam) will be carried out with particular attention to issues related to both robustness and ecological data. Improvements will then be made to mgcv so as to provide robust point estimates for the model parameters, as well as robustly obtained smoothing parameters. A new way of computing confidence intervals for the parameters that avoids the Bayesian approach available within mgcv will also be developed. Finally, issues including concurvity will be explored in an effort to make better tools available for performing model selection. Clustered count data with excess zeros is typical of the sort of data collected on endangered species, particularly in marine environments. Random effect hurdle models that allow for possibly overlapping sets of covariates for each part of the model as well as the prediction of cluster-specific targets will be developed. These models will allow ecologists to answer critical questions related to expected abundance.