Statistics and Applications

统计与应用

• 批准号: 0308609
• 负责人: Jiayang Sun
• 金额: $ 8.59万
• 依托单位: Case Western Reserve University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-08-01 至 2007-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0308609&HistoricalAwards=false
• 关键词: Statistics; Applications

Four research topics are pursued. The first is on inverse problems and measurement error models. New adaptive wavelet denoising for 3-dimensional objects will be studied and new non-Fourier deconvolution methods for measurement error models will allow users to take into account non-homogeneous errors that occur often in astronomical data. The second area is on biased sampling. Nonparametric and semi-parametric methods will be studied for data from multiple surveys and semi-parametric methods will be developed for survival data. The third area is on high dimensional graphics and data mining. Efficient methods and software will be developed for (large) data analysis and modeling. The fourth area is on mixture problems. New tests and model selection procedures are proposed.The challenges for statistics arising from astronomy, genetics, medical imaging and computer science are multifaceted. Data can be complex due to measurement errors or other unobservable features; or large in size or dimension due to advances in sciences and information technology; or small due to some intrinsic nature of data, for example, halos, ancient stars, are scarce in comparison to other stars. This project develops new theories, practical methods and efficient computational tools to meet these challenges, via the above four major research topics. The interdisciplinary nature of the research will impact our knowledge in the sciences. The research will also benefit education and human development, via training of students, integration with research and mentorship and collaboration with scientists.

四个研究课题正在进行。第一个是反问题和测量误差模型。将研究新的三维物体自适应小波去噪方法，新的测量误差模型非傅立叶反卷积方法将使用户能够考虑到天文数据中经常出现的非均匀误差。第二个领域是有偏抽样。将针对多项调查的数据研究非参数和半参数方法，并针对生存数据开发半参数方法。第三个领域是高维图形和数据挖掘。将为（大）数据分析和建模开发有效的方法和软件。第四个领域是混合问题。提出了新的检验和模型选择程序。来自天文学、遗传学、医学成像和计算机科学的统计挑战是多方面的。由于测量误差或其他不可观测的特征，数据可能很复杂;或者由于科学和信息技术的进步，数据可能很大;或者由于数据的某些内在性质，例如，晕，古老的恒星，与其他恒星相比是稀缺的。该项目通过上述四个主要研究主题，开发新的理论，实用方法和有效的计算工具来应对这些挑战。研究的跨学科性质将影响我们在科学方面的知识。这项研究还将通过培训学生、与研究和指导相结合以及与科学家合作，使教育和人类发展受益。