Statistics and Applications

研究课题有四个。第一部分是反问题和测量误差模型。将研究用于三维物体的新的自适应小波去噪和用于测量误差模型的新的非傅立叶反卷积方法，使用户能够考虑天文数据中经常出现的非均匀误差。第二个方面是关于有偏抽样。非参数和半参数方法将用于研究来自多个调查的数据，半参数方法将用于研究生存数据。第三个领域是高维图形和数据挖掘。将开发用于（大）数据分析和建模的有效方法和软件。第四个领域是关于混合问题。提出了新的试验和模型选择程序。天文学、遗传学、医学成像和计算机科学对统计学提出的挑战是多方面的。由于测量误差或其他不可观察的特征，数据可能很复杂；或由于科学和信息技术的进步而使规模或尺寸变大；或者是由于数据的某些固有性质，例如，光晕，古老的恒星，与其他恒星相比是稀缺的。本项目通过以上四个主要研究课题，开发新的理论、实践方法和高效的计算工具来应对这些挑战。这项研究的跨学科性质将影响我们在科学方面的知识。这项研究还将通过对学生的培训、与研究的整合以及与科学家的指导和合作，使教育和人类发展受益。

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.