Statistical Methodologies for High Dimensional Correlated Data

如今，各个学科的研究工作已经产生了不同于传统类型的复杂数据集。新的数据集可能具有高维数、大量参数、复杂的依赖关系或来自不同实验平台的测量结果。有一个越来越多的统计方法和推理程序的发展，以分析这些复杂的数据集的需求。我们计划进行理论研究，就如何开发统计方法，特别是设计用于高维相关数据。本文提出的新方法可用于解决统计遗传学和生物信息学领域的问题，如何正确地分析高维数据中复杂的依赖结构将是我们项目的主要动机，也是我们面临的主要挑战。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执行稀疏模型。在本研究计画中，我们将着重探讨相依资料的惩罚估计与模型选择方法。这些理论将为我们从数据中得出的推论提供更多的见解。特别是，该方法将使我们能够在大量数据中识别哪些信息是重要的。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。由于目前的技术在不同的平台上产生各种数据，因此非常需要这种程序。我们还将建立一个基于伪似然的通用框架来对相关群体进行遗传分析。我们期望发展这种统一的方法，这是普遍的广泛的遗传问题。

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 ofparameters, 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.