权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Statistical Modelling of Multivariate Functional and Distributional Data

多元函数和分布数据的统计建模

基本信息

批准号：
1811888
负责人：
Alexander Petersen
金额：
$ 14.99万
依托单位：
University of California-Santa Barbara
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2018
资助国家：
美国
起止时间：
2018-07-01 至 2021-04-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1811888&HistoricalAwards=false
关键词：
Statistical Modelling Multivariate Functional Distributional

项目摘要

Modern recording devices are collecting data of greater complexity and, when these data are measured over space or time, also at ever-increasing resolution. While providing more detailed information about the associated physical phenomena occurring around us, they also pose statistical challenges related to interpretable modeling and feasible computation for such data. Data measured over space, time, or some other continuum, are fittingly termed functional data, and constitute an important subfield of modern statistics. This project will develop important methodology for the analysis of two types of functional data. The first set of projects aim at the estimation of dependency patterns between components of so-called multivariate functional data, where a common set of features is measured over time for each subject in a study, such as neuroimaging scans where signals are recorded over time at a variety of spatial locations. Another important class of functional data are samples of distributions or histograms, which regularly arise in the analysis of demographic data as mortality distributions, for example, but also in other important fields such as neuroscience and finance. This project outlines methods for dimension reduction and regression that respect the well-known positivity and area-under-the-curve constraints for distributions, yielding interpretable data summaries and model fits that provide the practitioner with a clearer understanding of the information contained in their data.Both fMRI and EEG yield time-dependent signals at multiple brain locations, resulting in multivariate functional data. Quantifying connectivity patterns to define brain networks, for example in order to identify normal and pathological characteristics, is an important neuroscientific problem that can be addressed using multivariate functional data techniques. This project seeks to advance the use of functional graphical models to estimate underlying brain dependency networks, including improved computational efficiency compared to existing methods. These methods are equally applicable in other domains that produce data of similar structure, such as longitudinal medical studies, where a common set of measurements is recorded repeatedly over time. Also considered in this proposal are methods for distributional data, which can be thought of as collections of curves or surfaces, each corresponding to a probability distribution. For example, neuroimaging data naturally provide such distributional samples, as levels of myelination or signal correlations within brain regions are high-dimensional data that can be effectively summarized at the subject level by a histogram or distribution. Given a sample of such distributional data, this project investigates statistical methods of interpretable dimension reduction and dependency of distributional response functions on relevant covariates through distributional regression. A key tool is the Wasserstein metric for distributions, which has been widely successful in applied settings, but has not been utilized to its full extent in statistics.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.

现代记录设备正在收集更复杂的数据，当这些数据在空间或时间上进行测量时，分辨率也在不断提高。虽然提供了关于我们周围发生的相关物理现象的更详细的信息，但它们也提出了与此类数据的可解释建模和可行计算相关的统计挑战。在空间、时间或其他连续体上测量的数据被恰当地称为函数数据，构成了现代统计学的一个重要的子领域。该项目将为分析两种类型的功能数据开发重要的方法。第一组项目旨在估计所谓的多变量功能数据的组成部分之间的依赖模式，即随着时间的推移，为研究中的每个受试者测量一组共同的特征，例如神经成像扫描，其中信号随着时间的推移记录在不同的空间位置。另一类重要的函数数据是分布样本或直方图，它经常出现在人口统计数据的分析中，例如作为死亡率分布，但在神经科学和金融等其他重要领域也是如此。该项目概述了降维和回归的方法，这些方法尊重众所周知的正性和分布的曲线下面积限制，产生可解释的数据摘要和模型拟合，使从业者更清楚地了解他们的数据中包含的信息。fMRI和EEG在多个大脑位置产生时间相关的信号，从而产生多元函数数据。量化连接模式以定义大脑网络，例如为了识别正常和病理特征，是一个重要的神经科学问题，可以使用多变量函数数据技术来解决。该项目寻求推进功能图形模型的使用，以估计潜在的大脑依赖网络，包括与现有方法相比提高计算效率。这些方法同样适用于产生类似结构的数据的其他领域，例如纵向医学研究，其中随着时间的推移重复记录一组共同的测量数据。在该建议中还考虑了用于分布数据的方法，该方法可以被认为是曲线或曲面的集合，每条曲线或曲面对应于一个概率分布。例如，神经成像数据自然提供了这样的分布样本，因为脑区内髓鞘形成的水平或信号相关性是高维数据，可以通过直方图或分布在受试者水平上有效地总结。给出一个这样的分布数据样本，本项目通过分布回归研究了可解释降维和分布响应函数对相关协变量的依赖性的统计方法。一个关键的工具是分配的沃瑟斯坦指标，它在应用环境中得到了广泛的成功，但在统计中还没有得到充分的利用。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。