Statistical methods for space-time processes, time-frequency methodologies, and applications

时空过程统计方法、时频方法及其应用

• 批准号: 0906864
• 负责人: Peter Craigmile
• 金额: $ 12万
• 依托单位: Ohio State University Research Foundation -DO NOT USE
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-08-15 至 2012-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0906864&HistoricalAwards=false
• 关键词: Statistical; methods; space; time; processes

This project considers space-time models and time-frequency methods for the analysis of space-time data observed continuously (and often sparsely) in space, but discretely (and regular) in time. This research extends the spatially-dependent filtering approach used to define space-time processes to include space-time long memory processes, non-Gaussian processes, and non-linear processes. Since methods need to be developed for these types of statistical models that are efficient to use, part of this research focuses on statistical inference. A secondary study involves spectral and wavelet methods for the analysis of space-time processes. A spectral analysis is used to explore features of a statistical process in the frequency domain in terms of a linear combination of complex exponentials (sinusoids). A wavelet analysis provides a space/time-scale (approximately a space/time-frequency) decomposition of a statistical process in terms of averages and changes of averages over different temporal or spatial scales. Developing methods ofspectral- and wavelet-based exploratory data analysis and inference are of key interest.There is a growing need in many scientific areas to be able to understand phenomena that vary jointly across space and in time. Statistical methods are required in practice because these phenomena are observed in the presence of uncertainty. For example, Paleooclimatology (the history or "archaeology" of climate) involves obtaining surrogate measures for climatic variables over space that are valid over long time scales. Important scientific questions can be answered by relating data obtained from paleoclimatology to drivers of climate variability. The use of space-time statistical models and spectral and wavelet-based space-time analyses can inform how different temporal scales affect the climate relationships observed, and to understand how these relationships vary spatially. This research is directly applicable to other scientific areas, and results will be communicated via peer-reviewed articles in subject-matter as well as statistical areas. A diverse cross-section of students (statistical and non-statistical) will be mentored in methods of time series analysis and spatial statistics (via supervision and teaching).

这个项目考虑了时空模型和时频方法，用于分析在空间连续(通常是稀疏的)，但在时间上离散(和规则)的时空数据。本研究将用于定义时空过程的空间相关过滤方法扩展到包括时空长记忆过程、非高斯过程和非线性过程。由于需要为这些类型的统计模型开发有效使用的方法，因此本研究的部分重点是统计推断。二次研究涉及用于分析时空过程的谱方法和小波方法。频谱分析用于根据复指数(正弦)的线性组合来探索频域中统计过程的特征。小波分析提供了统计过程在不同时间或空间尺度上的平均值和变化的空间/时间尺度(约为空间/时间-频率)分解。开发基于光谱和小波的探索性数据分析和推断方法是非常有意义的。在许多科学领域，越来越需要能够理解在空间和时间上共同变化的现象。在实践中需要统计方法，因为这些现象是在存在不确定性的情况下观察到的。例如，古气候学(气候的历史或“考古学”)涉及获得在长时间尺度上有效的空间气候变量的替代测量。重要的科学问题可以通过将从古气候学获得的数据与气候变异性的驱动因素联系起来来回答。使用时空统计模型以及频谱和基于小波的时空分析可以了解不同的时间尺度如何影响观测到的气候关系，并了解这些关系在空间上如何变化。这项研究直接适用于其他科学领域，结果将通过同行评议的主题文章和统计领域的文章进行交流。将对不同领域的学生(统计和非统计)进行时间序列分析和空间统计方法的指导(通过监督和教学)。