Statistical Approaches for Complex Multi-Dimensional Data

本研究项目将开发模型和统计工具，用于分析复杂的多维时间数据。具有这些特征的数据通常出现在神经科学、环境科学和经济学等领域。目前，用于分析这些数据的统计工具存在局限性，特别是在神经影像学方面。一些常用的方法要么不能充分捕获这些数据背后的复杂结构，要么计算成本高，而且只在非常低维的环境中实际可行。这个项目将导致改进的方法，这些方法是通用的，因此适用于分析来自不同领域的数据。将为从事统计学与其他领域（如神经科学和环境科学）交叉研究的研究生提供新的教育和培训机会。实现新统计工具的开源软件将被开发出来并向公众开放。该研究项目将开发新的多元贝叶斯动态模型，用于联合分析和预测一组非平稳时间序列数据。这些模型和相关的计算工具将导致对表征每个单独时间序列的时变频谱特征的联合和快速推断，以及对集合中时间序列分量的时频关系的推断。动态层次模型分析多时间序列也将发展。分层方法将利用跨多个时间序列的强度对其共同的底层时频结构进行准确推断。将开发和实施这些多维时间模型设置中的稀疏性和降维工具。研究者将把新方法应用于脑成像数据、多通道脑电图数据、功能磁共振成像数据和多变量环境数据。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This research project will develop models and statistical tools for the analysis of complex multi-dimensional temporal data. Data with these characteristics commonly arise in fields such as neuroscience, the environmental sciences, and economics. Currently, there are limitations with the statistical tools available to analyze these data, particularly in neuroimaging. Some of the commonly used methods are either not able to adequately capture the complex structure underlying these data or are computationally expensive and only practically feasible in very low-dimensional settings. This project will result in improved methods that are general and therefore applicable to the analysis of data from a variety of fields. New educational and training opportunities will be provided to graduate students pursuing research at the interface between statistics and other areas such as neuroscience and the environmental sciences. Open-source software that implements the new statistical tools will be developed and made publicly available.The research project will develop new multivariate Bayesian dynamic models for joint analysis and forecasting of a collection of non-stationary time series data. These models and related computational tools will lead to joint and fast inference on the time-varying spectral features that characterize each individual time series, as well as inference on the time-frequency relationships across the time series components in the set. Dynamic hierarchical models for analysis of multiple time series also will be developed. The hierarchical approach will borrow strength across multiple time series to make accurate inferences on their common underlying time-frequency structure. Tools for sparsity and dimension reduction in these multi-dimensional temporal model settings will be developed and implemented. The investigator will apply the new methods to brain imaging data, multi-channel electroencephalogram data, fMRI data, and multivariate environmental data.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.