Statistical methods for large n and p problems

摘要现代生物学观测和实验数据经历了一场革命。在新的生物技术和计算技术进步的推动下，高维、高密度、功能多层次和纵向的生物信号在医学和公共卫生研究中越来越普遍。这些类型的信号历来发生在小型临床或实验环境中，通常被称为“小n，大p”问题。我们将这些生物信号扩展到纵向或分层结构的队列研究中，作为下一代生物统计学问题。我们称之为“大n大p分层”问题。这项资助的目的是介绍分析这种形式的生物统计数据的一般方法。我们提出了多层次或纵向采集的生物信号分析的三个主要目标。第一个扩展了多层次的功能主成分，研究者对功能主成分的概括，纵向和高维设置。第二种考虑研究者的双向过滤，并将其扩展到高维和纵向设置中。第三种方法考虑基于模型的独立分量盲源分离，并将其扩展到纵向设置。为了实现这一目标，我们还将考虑在高维参数空间中运行MCMC采样器的基本问题。具体来说，当参数数量大于迭代次数时，目前还没有关于收敛控制的工作。提出了一种利用有限总体抽样的收敛控制方法。我们的方法将应用于独特的数据集，包括成像（MRI, fMRI， DTI），电生理学（EEG， ECOG），睡眠测量（多导睡眠图）和新的衰老测量（加速度计）。在初步结果中，我们展示了我们在EEG， MRI和fMRI数据集分析中使用这些数据的新发现的能力。无监督聚类、盲源分离和降维等方法通常被认为是分析高维数据的第一步，并且已经成功地应用于各种各样的设置集合。我们的建议将这些基本方法推广到高维数据，同时考虑层次和纵向变化方向。因此，我们的方法将为下一代生物医学功能数据奠定基础。

DESCRIPTION (provided by applicant): Abstract Modern observational and experimental biological data has undergone a revolution. Driven by new biotechnology and computing advances, high dimensional, high density, functional multilevel and longitudinal biological signals are becoming commonplace in medical and public health research. These types of signals historically occurred in small clinical or experimental settings, often referred to as the "small n, large p" problem. We view the extension of these biological signals to cohort studies with longitudinal or hierarchical structure as a next generation of biostatistical problems. We've taken to calling this the "hierarchical large n, large p" problem. The goal of this grant is to introduce general methods for analyzing this form of biostatistical data. We propose three major aims for the analysis of multilevel or longitudinally collected biosignals. The first extends multilevel functional principal components, the investigators' generalization of functional principal components, to longitudinal and high dimensional settings. The second considers the investigators bi-directional filtering and extends it in high-dimensional and longitudinal settings. The third considers model-based independent component blind source separation and extends it to longitudinal settings. To solve this aim, we will also consider the fundamental problem of running MCMC samplers for high dimensional parameter spaces. Specifically, no current work exists for convergence control when the number of parameters is larger than the number of iterations. We propose a method of convergence control using finite population sampling. Our methods will be applied to unique data sets involving imaging (MRI, fMRI, DTI), electrophysiology (EEG, ECOG), sleep measurement (polysomnography) and novel measurements of aging (accelerometer). In the preliminary results, we demonstrate our capacity for working with such data with novel findings in the analysis of EEG, MRI and fMRI data sets. Methods such as unsupervised clustering, blind source separation and dimension reduction are generally recognized first steps in analyzing high dimensional data, and have been applied success- fully in an amazingly diverse collection of settings. Our proposal generalizes these basic approaches to high dimensional data while considering hierarchical and longitudinal directions of variation. Hence, our approaches will form a basic foundation for next generation biomedical functional data.