Time Series Analysis and Applications

本研究的重点是一些与时间序列分析应用相关的主题。 第一个项目的动机是DNA序列的分析。 其中一个重要的任务是翻译存储在DNA的蛋白质编码序列（CDS）中的信息。 分析长DNA序列数据的一个常见问题是识别分散在整个序列中并由非编码区域分隔的CDS。 众所周知，DNA序列是异质的，即使在DNA的短序列中，也会遇到局部行为。 在这个建议中，兴趣是在扩展的频谱包络的方法来捕捉这种序列的本地行为。 为了解决这个问题的局部行为的分类值时间序列，局部谱包络估计通过混合平滑样条将被探讨。 我们希望这种方法将有助于以快速和自动化的方式强调存在于几乎任何长度的分类序列中的任何周期性特征。 像人类基因组计划这样的项目已经产生了大量的数据。 据信，这些方法将被证明是有用的，在分析大量的数据正在产生的各种基因组计划。 该提案的另一个主要目标是通过开发类似于STARMAX模型的模型来探索时空建模。 目标是开发一种通用的方法，但研究将通过获得生物监视中困难问题的解决方案来管理，例如监测生物恐怖主义，以及医学中的困难问题，例如分析并发的EEG-fMRI记录。 虽然CDC等各种组织正在实时收集数据，但支持时间和空间数据分析和可视化的数据分析工具非常缺乏。 目前，大多数分析都是通过放弃（忽略或聚合）时间或空间来完成的。 几十年来，EEG一直是研究大脑的关键工具。 然而，尽管它有多种临床和研究用途，如癫痫，但对人类EEG活动的潜在发生器知之甚少。 功能性磁共振成像（fMRI）与脑电图记录一致，可以提供一种定位和识别这些来源的方法。 通过使用EEG信号作为fMRI图的参考，同步EEG-fMRI为研究特定的脑功能开辟了新的途径。 这项研究的重点是在时间，空间或顺序收集的数据的应用程序有关的一些主题。 第一个项目的动机是DNA序列的分析。 一项重要的任务是翻译存储在DNA蛋白质编码序列中的信息。 像人类基因组计划这样的项目已经产生了大量的数据。 据信，这些方法将被证明是有用的，在分析大量的数据正在产生的各种基因组计划。 该提案的另一个主要目标是通过开发新的统计模型来探索时空建模。 目标是开发一种通用的方法，但研究将通过获得生物监视中困难问题的解决方案来管理，例如监测生物恐怖主义，以及医学中的困难问题，例如分析并发的EEG-fMRI记录。 虽然CDC等各种组织正在实时收集数据，但支持时间和空间数据分析和可视化的数据分析工具非常缺乏。 目前，大多数分析都是通过丢弃（通过忽略或聚合）时间或空间来完成的。 几十年来，EEG一直是研究大脑的关键工具。 然而，尽管它有多种临床和研究用途，如癫痫，但对人类EEG活动的潜在发生器知之甚少。 功能性磁共振成像（fMRI）与脑电图记录一致，可以提供一种定位和识别这些来源的方法。 通过使用EEG信号作为fMRI图的参考，同步EEG-fMRI为研究特定的脑功能开辟了新的途径。

The focus of this research is on a number of topics relating to applications of time series analysis. The motivation for the first project is the analysis of DNA sequences. One important task is to translate the information stored in the protein-coding sequences (CDS) of the DNA. A common problem in analyzing long DNA sequence data is in identifying CDS that are dispersed throughout the sequence and separated by regions of noncoding. It is well known that DNA sequences are heterogeneous, and even within short subsequences of DNA, one encounters local behavior. In this proposal, the interest is in extending the spectral envelope methodology to capture the local behavior of such sequences. To address this problem of local behavior in categorical-valued time series, local spectral envelope with estimation via mixtures of smoothing splines will be explored. It is the hope that this methodology will help emphasize any periodic feature that exists in a categorical sequence of virtually any length in a quick and automated fashion. Projects such as the human genome project have produced large amounts of data. It is believed the methods will prove to be useful in the analysis of the vast quantities of data being produced by various genome projects. Another primary objective of this proposal is to explore spatio-temporal modeling by developing models similar to the STARMAX model. The goal is to develop a general methodology, but the research will be governed by obtaining solutions to difficult problems in biosurveillance, such as monitoring bioterrorism, and in medicine, such as the analysis of concurrent EEG-fMRI recordings. Although data is being collected in real-time by various organizations such as the CDC, data analytic tools that support both temporal and spatial data analysis and visualization are sorely lacking. At the present time, most analysis is accomplished by dropping (either by ignoring or by aggregating) either time or space. EEG has been a key tool in the study of the brain for decades. However, despite its multiple clinical and research uses, such as in epilepsy, little is yet known about the underlying generators of EEG activity in humans. Functional MRI (fMRI) recorded in concert with EEG may provide a method for localizing and identifying these sources. By using the EEG signal as a reference for fMRI maps, concurrent EEG-fMRI opens a new avenue for investigating specific brain function. The focus of this research is on a number of topics relating to applications of data collected in time, in space, or in sequence. The motivation for the first project is the analysis of DNA sequences. One important task is to translate the information stored in the protein-coding sequences of the DNA. Projects such as the human genome project have produced large amounts of data. It is believed the methods will prove to be useful in the analysis of the vast quantities of data being produced by various genome projects. Another primary objective of this proposal is to explore spatio-temporal modeling by developing new statistical models. The goal is to develop a general methodology, but the research will be governed by obtaining solutions to difficult problems in biosurveillance, such as monitoring bioterrorism, and in medicine, such as the analysis of concurrent EEG-fMRI recordings. Although data is being collected in real-time by various organizations such as the CDC, data analytic tools that support both temporal and spatial data analysis and visualization are sorely lacking. At the present time, most analysis is accomplished by dropping (either by ignoring or by aggregating) either time or space. EEG has been a key tool in the study of the brain for decades. However, despite its multiple clinical and research uses, such as in epilepsy, little is yet known about the underlying generators of EEG activity in humans. Functional MRI (fMRI) recorded in concert with EEG may provide a method for localizing and identifying these sources. By using the EEG signal as a reference for fMRI maps, concurrent EEG-fMRI opens a new avenue for investigating specific brain function.