Local Likelihood Estimation for Nonstationary Random Fields

非平稳随机场的局部似然估计

• 批准号: 1007480
• 负责人: Ethan Anderes
• 金额: $ 14.88万
• 依托单位: University of California-Davis
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-07-15 至 2014-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1007480&HistoricalAwards=false
• 关键词: Local; Likelihood; Estimation; Nonstationary; Random

Stationary random fields play a fundamental role in both theoretical and applied spatial statistics. Unfortunately, stationarity is often violated when working with real data. This presents a challenge for the spatial statistician who is interested in estimating and modeling dependence structure in random fields. The investigator and his collaborator will study, and subsequently apply, a recently developed version of local likelihood estimation for estimating parameters that govern the local dependency in nonstationary random fields. The application is to use local likelihoods for the estimation of the local distortion of the cosmic microwave background (CMB) due to gravitational lensing. Detecting and estimating this lensing is important for two reasons. First, measuring the distortion gives an indirect measurement of matter in the Universe which can provide detailed maps of the distribution of Dark Matter. Secondly, one can use the estimates of gravitational lensing to obtain a more accurate measurement of the un-lensed CMB. This will provide scientists with a deeper probe of fundamental cosmological questions. Specific aims of this proposal include: 1) develop computational techniques which will make local likelihood estimation applicable to large data sets such as the CMB; 2) develop the theory of estimating equations for local weight construction with a particular focus on mitigating bias and automatically adjusting for boundaries and uneven observation locations; 3) construct estimates of uncertainty in the local likelihood estimates of the parameter function; 4) use the principle irregular term to develop flexible and universal local models for general nonstationary random fields. Nonstationary random fields are becoming a ubiquitous feature in the recent data deluge and high resolution sensing. Unfortunately, the techniques for modeling, estimating and predicting nonstationary random fields have yet to be fully developed and analyzed. This proposal will make steps towards the goal of developing a complete set of methodological techniques for analyzing nonstationary random fields. Moreover, the tools thus constructed will be useful, not only for Astronomy and Cosmology, but other branches of science and technology as well. This makes the broader impact of the scientific consequences of this proposal two fold. On the one hand, accurately estimating gravitational lensing in the CMB has far reaching consequences for the understanding of cosmic structure and the beginnings of the Universe. On the other hand, the tools from this project are expected to have broad use in other areas of real world application. Recently developed technologies such as fMRI and diffusion tensor imaging are two examples of other scientific areas that will benefit from the methodologies developed for nonstationary random fields.

平稳随机场在理论和应用空间统计中起着重要的作用。不幸的是，在处理真实的数据时，经常违反平稳性。 这对有兴趣估计和建模随机场依赖结构的空间统计学家提出了挑战。研究人员和他的合作者将研究，并随后应用，最近开发的版本的本地似然估计估计参数，管理本地的依赖性在非平稳随机场。 该应用程序是使用本地似然估计的宇宙微波背景（CMB）由于引力透镜的本地失真。检测和估计这种透镜效应很重要，原因有二。首先，测量扭曲可以间接测量宇宙中的物质，从而可以提供暗物质分布的详细地图。其次，可以使用引力透镜的估计来获得非透镜CMB的更精确的测量。这将为科学家提供对基本宇宙学问题的更深入探索。 该提案的具体目标包括：1）开发计算技术，使局部似然估计适用于大型数据集，例如CMB; 2）开发局部权重构建的估计方程理论，特别关注减轻偏差并自动调整边界和不均匀的观察位置; 3）在参数函数的局部似然估计中构造不确定性的估计：4）利用主非正则项建立了一般非平稳随机场的灵活而通用的局部模型。非平稳随机场在近年来的数据洪流和高分辨率传感中正成为一个普遍存在的特征。 不幸的是，非平稳随机场的建模，估计和预测技术尚未得到充分的发展和分析。该建议将为发展一套完整的分析非平稳随机场的方法学技术的目标迈出一步。此外，这样构建的工具不仅对天文学和宇宙学有用，而且对其他科学和技术分支也有用。 这使得这一提议的科学后果的更广泛影响具有双重性。一方面，准确估计CMB中的引力透镜效应对于理解宇宙结构和宇宙起源具有深远的影响。另一方面，该项目的工具预计将在真实的世界应用的其他领域得到广泛使用。最近开发的技术，如功能磁共振成像和扩散张量成像是其他科学领域的两个例子，将受益于为非平稳随机场开发的方法。