Nonparametric Methods for Temporally Correlated and High Dimensional Data

用于时间相关和高维数据的非参数方法

• 批准号: RGPIN-2014-04311
• 负责人: Takahara, Glen
• 金额: $ 0.8万
• 依托单位: Queen's University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635819
• 关键词: Nonparametric; Methods; Temporally; Correlated; Dimensional

Progress in modern statistical methods remains vital in the face of challenges put forth by ever increasing amounts of data, the need to obtain accurate information from data that is increasingly pivotal in important decision processes, and the opportunities afforded by increased computing power. Nonparametric statistical methods, which is to say methods that place few and very weak assumptions on the data, are attractive in virtually every field of application for their broad applicability.The proposed research falls in this area and centres on developing theory and applications in nonparametric Bayesian methods, spectral methods for time series, and the reduction of high dimensional data. These are three distinct areas within statistics of active current research, dealing with qualitatively different types of data.Inference in Bayesian nonparametric methods, like all Bayesian methods, is based on a passage from a prior distribution to a posterior distribution over the quantity of interest which in the nonparametric case is not finite-dimensional. Examples are an unknown distribution, density function, or survival function. The desirable features of such methods are freeness from assumptions that the unknown quantity follows some parametric form as well as the wide range of inference possible once the posterior distribution is obtained in a workable form. The challenge with such methods is the theory and computation necessary to give posterior representations that are feasible to work with so as to draw inference from these representations efficiently. Spectral methods in time series analyze the data in the frequency domain. Some of the challenges in modern spectral methods include the problem of frequency aliasing and the difficult problems associated with nonstationary time series, including estimation of time varying spectra and testing for different forms of nonstationarity. A more pragmatic challenge involves the introduction of such methods into fields where such methods are traditionally not used, and we focus on environmental health risk and environmental epidemiolgy. The challenge in processing of high-dimensional data in statistics is to identify low dimensional structure in the data (which generally will be nonlinear) that can then be used to give a low dimensional representation while retaining the salient features of the data. TheThe work proposed here will address all of these challenges and lead to high quality, original research that will further the theory and applications in nonparametric statistical methods. The work in nonparametric Bayesian methods will give insight into the structure of posterior representations that will give rise to new computational methods for inference and grouping of data structure. The work in spectral methods for time series will advance methods for dealing with aliasing effects and nonstationarity in time series, which has wide ranging potential downstream implications, not the least of which is a better understanding of the processes defining our physical world. A further downstream impact will be to refine and improve the interpretability and reliability of risk estimation in the fields of environmental health risk and environmental epidemiology, which can ultimately affect the policies we make that pertain to the health of Canadians. The work in reduction of high dimensional data is ultimately a step towards opening up powerful statistical methodologies designed for low dimensional data to the ever increasing complexities of modern data.Training is a major component of this research program, which will support 5 Phd and 5 MSc graduate students, 4 undergraduate summer research students, and 2 to 3 Postdoctoral Fellows in total.

面对越来越多的数据所带来的挑战，现代统计方法的进展仍然至关重要，需要从重要的决策过程中越来越关键的数据中获得准确的信息，以及计算能力增加所带来的机会。非参数统计方法是说，在数据上几乎每个应用领域都具有很少的假设和非常弱的假设的方法，以实现其广泛的适用性。拟议的研究属于该领域，并集中在非参数贝叶斯方法中的理论和应用集中，该方法是时间序列的光谱方法，以及高度上限数据的降低。这是现有当前研究统计统计中的三个不同领域，处理质量不同的数据。与所有贝叶斯方法一样，贝叶斯非参数方法的指定是基于从先前分布到后验分布的段落，而不是在非参数情况下的兴趣量，这不是有限的。示例是未知的分布，密度函数或生存功能。此类方法的理想特征是从未知数量遵循某些参数形式以及一旦以可工程形式获得后验分布的广泛推理的假设。这种方法面临的挑战是提供可行的后验表示所需的理论和计算，以便有效地从这些表示形式中提取推断。时间序列中的光谱方法分析了频域中的数据。现代光谱方法中的某些挑战包括频率混叠问题以及与非组织时间序列相关的困难问题，包括估计时间变化的光谱和测试不同形式的非组织性。更务实的挑战涉及将这种方法引入传统上不使用此类方法的领域，我们专注于环境健康风险和环境流行病。统计数据中高维数据处理的挑战是确定数据中的低维结构（通常是非线性），然后可以使用该结构来给出低维表示，同时保留数据的显着特征。这里提出的工作将解决所有这些挑战，并带来高质量的原始研究，这将进一步进一步，以进一步促进非参数统计方法中的理论和应用。非参数贝叶斯方法中的工作将洞悉后表示的结构，这些结构将引起新的计算方法，以推断和分组数据结构。时间序列的光谱方法的工作将推进处理混音效应和时间序列中的非叠加效果的方法，该方法具有广泛的潜在下游含义，而不是其中的范围很广，而不是最好的理解对定义我们物理世界的过程有更好的理解。在环境健康风险和环境流行病学领域，进一步的下游影响是提高和提高风险估计的可解释性和可靠性，这最终可能会影响我们制定的与加拿大人健康有关的政策。降低高维数据的工作最终是迈出的一步，旨在开放强大的统计方法论，旨在为低维数据旨在为现代数据的越来越多的复杂性而设计。培训是该研究计划的主要组成部分，该计划将支持5年级和5名MSC研究生，4名本科生的夏季研究生和2至3个博士后研究员。