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

该研究计划的重点是为表现出空间和/或时间依赖性的数据开发统计方法，特别关注对生态学重要的内容。状态空间模型（SSM）正在成为分析动物跟踪数据的标准工具，但可能是计算密集型的，难以实现，特别是当涉及参数估计。提出了MATLAB中的粒子滤波方法来实现用于跟踪数据的SSM，从而a）极大地促进了复杂环境数据的集成，B）实现在线拟合，以及c）允许通过状态增强来估计时变参数。 这样一来，生态学家就更容易接触到SSM，从而有可能提出关于动物如何与其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，但对偏离假设模型的观测值的存在非常敏感。首先，正式比较两种流行的方法，以适应在R（mgcv和gam）将进行特别注意的问题，有关的鲁棒性和生态数据。然后将改进mgcv，以便提供稳健的点估计模型参数，以及稳健地获得平滑参数。还将开发一种新的方法来计算参数的置信区间，以避免mgcv中可用的贝叶斯方法。最后，将探讨包括并发性在内的问题，以便为执行模型选择提供更好的工具。在收集濒危物种的数据时，特别是在海洋环境中，经常会收集到带有多余零的计数数据。将开发随机效应障碍模型，该模型允许模型每个部分的协变量集可能重叠，以及预测集群特定的目标。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.****