Statistical Methodologies for High Dimensional Correlated Data

如今，不同学科的研究努力产生了不同于传统类型的复杂数据集。新类型的数据集可能具有高维、大量的 参数，复杂的依赖关系，或来自不同实验平台的测量。人们越来越需要开发统计方法和推论程序来分析这些复杂的数据集。我们计划就如何开发专门为高维相关数据设计的统计方法进行理论研究。提出的新方法可以用来解决统计遗传学和生物信息学领域中出现的问题。 在存在复杂依赖结构的情况下正确分析高维数据将是我们项目的主要动机和主要挑战。为了降低问题的维度，有许多策略，包括选择一个更简单的子模型，或者通过惩罚来强制实施稀疏模型。在本研究项目中，我们将重点研究相依数据的惩罚估计和模型选择方法。这些理论将为我们从数据中得出的推断提供更多的洞察力。特别是，该方法将使我们能够在海量数据中辨别出哪些信息是重要的。在我们项目的应用方面，我们将研究执行数据集成的不同方法。这种程序非常需要，因为目前的技术在不同的平台上产生各种类型的数据。我们还将致力于建立一个基于伪似然的通用框架，对相关群体进行遗传分析。我们希望开发这种统一的方法，它对广泛的遗传问题是通用的。

Nowadays research efforts in various disciplines have generated complex data sets different from the traditional types. The new kinds of data sets may have high-dimensionality, a large number of parameters, complicated dependency relationship, or measurements from different experimental platforms. There is an increasing demand for the development of statistical methodologies and inference procedures to analyze these complex data sets. We plan to conduct theoretical investigations on how to develop statistical methods especially designed for high dimensional correlated data. The proposed new methods can be used to address the problems arising from the fields of statistical genetics and bioinformatics. To properly analyze high dimensional data in the presence of complex dependency structure will be the main motivation and also the major challenge for our project. To reduce the dimensionality of the problem, there are a number of strategies, including selecting a simpler sub-model, or enforcing a sparse model through penalization. In this research project, we will focus on the investigation of penalized estimation and model selection methods for dependent data. The theories will provide more insight into the inference we can draw from data. Especially, the method will enable us to discern which pieces of information are important among huge amount of data. On the applied side of our project, we will be investigating different methods to perform data integration. Such procedures are in great need because current technologies produce various kinds of data in different platforms. We will also aim to set up a general framework based on pseudo likelihood to perform genetic analysis for correlated populations. We expect to develop this unified approach which is general for a wide range of genetic problems.