Random Processes: Data Analysis and Theory

随机过程：数据分析和理论

• 批准号: 0504162
• 负责人: David Brillinger
• 金额: --
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-06-01 至 2009-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0504162&HistoricalAwards=false
• 关键词: Random; Processes; Data; Analysis; Theory

Random process data analysis has become a major theme of contemporary science. Motivated by problems from wildlife biology and forestry, techniques for the statistical handling of spatial-temporal point process data and of curved trajectories in the plane are developed as well as statistical methods for random process data generally. In particular probabilists have discovered various theoretical results concerning vector-valued stochastic differential equations, but their statistical and data analytic properties have not been totally developed. Stochastic differential equations are employed to describe the observed trajectories of the animals in the reserve. The equations are unusual in having paths of explanatories included and sometimes time lags. The fact that an animal's motion is bounded by a high fence also affects the analysis. In the work approximations to the random model are needed. The large sample accuracy of the approximations will be studied. The tools of point processes, smoothing and time series analysis are being employed with the wildfire data. Predictors of future risk and possible loss as the fire season proceeds and for future years are being developed.Two specific problems addressed are of broad impact and of societal importance. The problems are risk estimation for wildfires and the investigation of the effects that humans moving through an animal reserve have on the behavior of the animals. A question in the latter case is with what level of human usage can wild animals and humans share a habitat. There are data available from designed experiments with humans walking, riding horses, bicycling and on all-terrain vehicles traveling in the reserve. Both problems are studied using data sets come from the Forest Service, U. S. Department of Agriculture. This work is of particularly broad impact for there are the possibility of reducing human threat from fire, and of maintaining natural resource values. Predictions of the risk as a function of time and space will allow efficient placement of fire fighting resources.The intellectual merit of the work includes that quite a variety of interesting analytic problems arise, motivated by these applications, and these problems will be addressed in the research. The data sets are large so it is anticipated that real progress will be made on understanding the applicability of the methods.

随机过程数据分析已成为当代科学的一个重要主题。受野生生物学和林业问题的启发，发展了时空点过程数据和平面曲线轨迹的统计处理技术，以及随机过程数据的统计方法。特别是关于向量值随机微分方程，概率学家已经发现了各种理论结果，但它们的统计和数据分析性质还没有完全发展。采用随机微分方程来描述动物在保护区的观察轨迹。方程是不寻常的，包括路径的天文台，有时时间滞后。事实上，动物的运动是由一个高围栏限制也影响分析。在工作中，需要对随机模型进行近似。将研究近似值的大样本精度。点处理，平滑和时间序列分析的工具正在与野火数据。随着火灾季节的进行和未来几年的未来风险和可能损失的预测器正在开发中，所处理的两个具体问题具有广泛的影响和社会重要性。这些问题是野火的风险估计和人类通过动物保护区对动物行为的影响的调查。在后一种情况下的一个问题是，在什么程度的人类利用下，野生动物和人类可以共享一个栖息地。有数据可从设计的实验与人类步行，骑马，骑自行车和全地形车在保护区旅行。这两个问题的研究使用的数据集来自林务局，美国。S.农业部。这项工作具有特别广泛的影响，因为有可能减少火灾对人类的威胁，并保持自然资源的价值。作为时间和空间的函数的风险预测将允许有效地安置消防resources.The智力价值的工作包括，相当多种有趣的分析问题出现，这些应用程序的动机，这些问题将在研究中得到解决。数据集很大，因此预计在了解这些方法的适用性方面将取得真实的进展。