Statistical Inference for Large-Scale Structured Data with Dependence and Non-Stationarity

该项目旨在解决一些具有挑战性的研究问题，其共同主题是利用大规模结构化数据中的时空相关性和非平稳性，这些数据来自生物学、遗传学、天文学、经济学、神经科学、地球物理学和气象学等科学研究。将开发新的工具，用于随机建模、计算算法和统计推断，应用于医学成像数据，如功能磁共振成像、神经元棘波训练、全基因组关联研究，以及建立更快的文件访问系统。预计这些新的发展将使科学家能够以显著提高的灵活性和准确性有效地分析数据，从而对科学、公共卫生和信息技术的这些应用产生直接影响。这项研究还将通过开发一门关于分析空间和时间相关成像数据的新统计方法的研讨会课程，与教育实践相结合。该项目的重点是充分容纳三种根本不同类型的时空依赖结构。这些研究成果旨在弥合现有有限的理论和方法与许多应用领域遇到的广泛和具有挑战性的科学问题之间的差距。在fMRI数据分析的启发下，项目1探索了一种新的半参数推理方法，适用于在给定空间点收集的时程数据的一类广泛的非平稳、非高斯时间依赖的误差过程。提出了一种新的检验统计量，并建立了它的渐近性质。大规模的多个测试任务往往表现出相关性，而个体非高斯检验统计量之间的相关性的解释是统计学中一个重要的、具有挑战性的但尚未解决的问题。在从功能磁共振成像研究中检测激活的大脑区域以及评估单核苷酸多态与GWAS研究中的一种疾病之间的关联方面的挑战的推动下，项目2提出了一个新的多重测试框架，用于不同数量的“具有任意依赖结构的相关卡方检验统计”。受在时间和空间上具有相关性的多个神经脉冲训练记录中的应用的启发，项目3开发了新的综合方法来学习在具有非平稳事件时间的多变量点过程数据的广泛类别下的节点之间的“稀疏网络结构依赖”。

This project aims to address some challenging research problems, with a common theme of exploiting spatial-temporal dependence and non-stationarity in large-scale structured data, emerging from scientific studies in biology, genetics, astronomy, economics, neuroscience, geophysics, and meteorology among others. New tools will be developed for stochastic modeling, computational algorithms, and statistical inference applied to medical imaging data such as functional magnetic resonance imaging, neuron spike trains, genome-wide association studies, and building faster file access systems. It is anticipated that these new developments will allow scientists to efficiently analyze data with significantly increased flexibility and accuracy, and thus will have direct impacts on these applications to science, public health, and information technology. The research will also be integrated with educational practice through development of a seminar course on new statistical methods for analyzing spatially and temporally correlated imaging data. The project focuses on adequate accommodation of three fundamentally different types of spatial-temporal dependence structures. The research results aim to bridge the gap between the limited theory and methodology currently available and the broad and challenging scientific problems encountered in many applied fields. Motivated by fMRI data analysis, Project 1 explores a new semi-parametric inference procedure applicable to a broad class of "non-stationary non-Gaussian temporally dependent" error processes for time-course data collected at a given spatial point. A new test statistic will be developed, and its asymptotic properties will be established. Large-scale multiple testing tasks often exhibit dependence, and accounting for the dependence among individual non-Gaussian test statistics is an important, challenging, but unsolved problem in statistics. Motivated by challenges in detection of activated brain regions from fMRI studies and assessing association between single-nucleotide polymorphisms and a disease from GWAS studies, Project 2 proposes a new multiple testing framework for a diverging number of "correlated chi-squared test statistics with an arbitrary dependence structure." Motivated by applications in multiple neural spike train recordings with dependence in both time and space, Project 3 develops new integrative methods for learning the "sparse network structured dependence" among nodes underlying a wide class of multivariate point process data with non-stationary event times.