Statistical Inference for Tree Models with Strong Hierarchical Autocorrelation

具有强层次自相关的树模型的统计推断

• 批准号: 1106483
• 负责人: Cecile Ane
• 金额: $ 20.65万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-07-01 至 2015-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1106483&HistoricalAwards=false
• 关键词: Statistical; Inference; Tree; Models; Strong

Models with tree-structured, hierarchical autocorrelation are used when sampling units are related to each other. Their inheritance history is modeled by a tree, which is used to parametrize the residual correlation structure among observations. The project will develop an asymptotic theory for these autocorrelation models, arising from an Ornstein-Uhlenbeck process along the tree. As the number of tips in the tree grows indefinitely, the investigators will determine which parameters are microergodic and which parameters are not. The asymptotic consistency and the rate of convergence of the maximum likelihood estimator are expected to vary importantly depending on the microergodicity of the parameter and on topological properties of the tree. Analogies will be built between this asymptotic framework and the infill asymptotic framework in spatial statistics, when observations are collected on a dense set of locations within a bounded region of space. The project will refine the concept of effective sample size for hierarchically autocorrelated data and study optimal sampling designs. This work will provide important steps toward developing appropriate model selection tools for the detection of possibly many Ornstein-Uhlenbeck selection regimes, with a large number of model parameters compared to the sample size. Tree models with hierarchical autocorrelation arose first in evolutionary biology and ecology, with the comparison of biological species. These models are now used in many other areas, ranging from the study of rapidly evolving viruses to the study of human language evolution. The Ornstein-Uhlenbeck model is used to detect selection as opposed to neutral evolution, to discover changes in selective regime and to determine driving factors of selection. The project will provide a unified statistical asymptotic framework for these models and will inform best practices for empirical studies. Computational tools will be broadly disseminated, and opportunities will be provided for training at the interface between statistics and biology.

当采样单元彼此相关时，使用具有树结构、分层自相关的模型。它们的继承历史由树来建模，该树用于参数化观测之间的残差相关结构。该项目将开发这些自相关模型的渐近理论，从一个奥恩斯坦-乌伦贝克过程沿着树。随着树中的尖端数量无限增长，研究人员将确定哪些参数是微遍历的，哪些参数不是。的渐近一致性和收敛速度的最大似然估计预计会有很大的不同，这取决于参数的微观遍历性和拓扑性质的树。类比将建立在这个渐近框架和填充渐近框架的空间统计，当观察收集在一个有界的空间区域内的一组密集的位置。该项目将完善分层自相关数据的有效样本量概念，并研究最佳抽样设计。这项工作将提供重要的步骤，开发适当的模型选择工具，用于检测可能有许多奥恩斯坦-乌伦贝克选择制度，与大量的模型参数相比，样本量。具有层次自相关的树模型首先出现在进化生物学和生态学中，用于生物物种的比较。这些模型现在被用于许多其他领域，从研究快速进化的病毒到研究人类语言进化。Ornstein-Uhlenbeck模型用于检测选择，而不是中性进化，以发现选择机制的变化，并确定选择的驱动因素。该项目将为这些模型提供一个统一的统计渐近框架，并为实证研究提供最佳做法。 将广泛传播计算工具，并将提供统计与生物学之间接口的培训机会。