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

该项目考虑分析在空间上连续（通常稀疏）但在时间上离散（和规则）观测的时空数据的时空模型和时间频率方法。 这项研究扩展了用于定义时空过程的空间相关滤波方法，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，因此本研究的一部分集中在统计推断上。 次级研究涉及用于分析时空过程的谱方法和小波方法。 频谱分析是用来探索在频域中的复指数（正弦曲线）的线性组合的统计过程的功能。 小波分析根据不同时间或空间尺度上的平均值和平均值的变化提供统计过程的空间/时间尺度（近似空间/时间-频率）分解。 发展基于光谱和小波的探索性数据分析和推断方法是关键的兴趣。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措施。 重要的科学问题可以通过将古气候学获得的数据与气候变化的驱动因素联系起来来回答。 使用时空统计模型以及基于光谱和小波的时空分析可以告知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，结果将通过主题和统计领域的同行评议文章进行交流。 学生（统计和非统计）的不同横截面将在时间序列分析和空间统计（通过监督和教学）的方法辅导。

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).