Collaborative Research: Spectral and Connectivity Analysis of Non-Stationary Spatio-Temporal Data

这项研究的重点是开发新的统计方法来模拟非平稳时空数据的连通性。调查人员将开发四种具体的方法和模型，这些方法和模型将应用于调查人员合作者提供的数据。首先，由于需要更复杂的方法来研究两个时间序列(例如，大脑区域)之间的复杂相关性，研究人员将建立工具，使用谱域中的动态互信息来探索信号之间的非线性和时间演化相关性。其次，空间变化和时间演化频谱的概念将通过非平稳时空过程的随机表示而变得精确。将开发一个一致估计和推理的渐近框架。第三，通过潜在网络模型，建立多对象实验中连通性的一般谱模型。经验驱动的模型将包括刺激类型、外生时间序列和特定于受试者的随机效应等项目。最后，为了补充这种模拟光谱数据和连通性的探索性方法，研究人员将使用多学科数据建立一个基于科学动机的有效连通性的半参数状态空间模型。这项研究的总体目标是开发新的统计方法来分析同时具有时间和空间维度的数据。时空数据在许多学科中很普遍，包括环境和土壤科学、气象学和海洋学、神经科学以及卫生和生物恐怖主义监测等新兴领域。研究人员的主要数据来源是在大脑中许多位置测量的大脑活动的时序数据。这些信号包含有关大脑如何运作、它如何对外界刺激做出反应以及功能同步发生在哪里的信息。研究人员正在开发的统计模型有助于筛选这些信息，从而能够检测大脑功能的趋势，并估计人群和个人水平的表现差异。这些模型的经验性质允许数据驱动的神经科学理论的确认和发现。统计模型还将具有预测性，有助于寻求对抑郁、焦虑和其他神经疾病的个性化诊断和治疗。虽然统计研究的动机是调查人员与神经科学家的持续合作，但有一个统一的统计主题适用于许多其他感兴趣的领域。

The focus of this research is the development of new statistical methodologies for modeling connectivity in non-stationary spatio-temporal data. The investigators will develop four specific methods and models which will be applied to data provided by t he investigator's collaborators. First, motivated by the need for more sophisticated methods to investigate complex dependencies between two time series (e.g., brain regions), the investigators will build tools for exploring non-linear and time-evolving dependence between signals using dynamic mutual information in the spectral domain. Second, the notion of spatially-varying and temporally-evolving spectrum will be made precise via a stochastic representation of non-stationary spatio-temporal processes. An asymptotic framework for consistent estimation and inference will be developed. Third, a general spectral model for connectivity in a multi-subject experiment via a latent network model will be formulated. The empirically-driven model will incorporate items such as stimulus types, exogeneous time series, and subject-specific random effects. Finally, to complement this exploratory approach for modeling spectral data and connectivity, the investigators will build a scientifically-motivated semi-parametric state-space model of effective connectivity using multi-subject data.The overarching goal of this research is the development of new statistical methodologies for analyzing data that has both a time and space dimension. Spatio-temporal data are prevalent in many disciplines, including the environmental and soil sciences, meteorology and oceanography, neuroscience and the emerging fields of health and bioterrorism surveillance. The primary data source for the investigators is time-sequenced data of brain activity measured at many locations in the brain. These signals contain information on how the brain functions, how it responds to outside stimuli, and where synchronization of functionality occurs. The statistical models the investigators are developing help sift through this information, allowing for the detection of trends in brain functionality, and estimation of population- and individual-level differences in performance. The empirical nature of the models allows for data-driven confirmation and discovery of neuroscientific theory. The statistical models will also be predictive, aiding in the quest for personalized diagnosis and treatment of depression, anxiety, and other neurological conditions. While the statistical research is motivated by the investigators' ongoing collaboration with neuroscientists, there is a unified statistical theme applicable to many other areas of interest.