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

本研究建议的中心是发展显示空间和/或时间依赖性的数据的统计方法，对生态学的重要性特别感兴趣。**状态空间模型（ssm）正在成为分析动物跟踪数据的标准工具，但可能需要大量的计算并且难以实现，特别是当涉及参数估计时。提出了MATLAB中的粒子滤波方法来实现跟踪数据的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，c)允许通过状态增强估计时变参数。这样，生态学家就更容易接触到ssm，从而有可能提出有关动物如何根据环境移动的重要问题。**广义加性模型（GAMs）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结果非常敏感。首先，将对R中拟合GAMs的两种流行方法（mgcv和gam）进行正式比较，并特别关注与鲁棒性和生态数据相关的问题。然后将对mgcv进行改进，以便为模型参数提供鲁棒的点估计，以及鲁棒获得的平滑参数。还将开发一种新的计算参数置信区间的方法，该方法避免了在mgcv中可用的贝叶斯方法。最后，我们将探讨包括共通性在内的问题，以便为执行模型选择提供更好的工具。**带有多余零的聚类计数数据是收集濒危物种的典型数据，特别是在海洋环境中。将开发随机效应障碍模型，该模型允许模型的每个部分可能重叠的协变量集以及集群特定目标的预测。这些模型将允许生态学家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.****