Central Project: Research Unit Structural Inference in Statistics: Adaption and Efficiency

中心项目：统计中的研究单位结构推理：适应和效率

• 批准号: 213998942
• 负责人: Professorin Dr. Natalie Neumeyer
• 金额: --
• 依托单位: Bereich Mathematische Statistik und Stochastische Prozesse
• 依托单位国家: 德国
• 项目类别: Research Units
• 财政年份: 2012
• 资助国家: 德国
• 起止时间: 2011-12-31 至 2019-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/213998942?language=en
• 关键词: Central; Project; Research; Unit; Structural

Because of the increasing availability of data, statistics plays a more and more prominent role in many scientific and practical areas. On the other hand, the most general realistic models are usually very complex such that poor statistical precision is very common in spite of the large amount of data. The Hamburg-Berlin-Potsdam Research Unit Structural Inference in Statistics: Adaptation and Efficiency aims at developing new methods and tools to profit from structures underlying high-dimensional complex data. Structure not only concerns the unknown targets of inference (involving smoothness, sparsity or low dimensions), but also the data structure involving unknown correlation matrices, hierarchical or multiscale interaction or support properties of the noise. The long-term goal is to establish a general framework to adapt automatically and simultaneously to different structures that might be present in the data. This will allow for much more efficient statistical procedures, which will have a strong impact on the significance of statistical results in a wide range of applications. Moreover, the gained fundamental insight will often allow a quick transfer of efficient methods to new structures in upcoming applications. The advanced new tools developed for the mathematical analysis will push on the whole field of mathematical statistics for complex structural models. The research unit comprises eight principal investigators from the University of Hamburg, Humboldt-Universität zu Berlin, Weierstraß Institute Berlin and the University of Potsdam. Their joint expertise in different areas of statistics is focussed on modern efficient methods which are analysed using advanced mathematical theory and are applicable to a wide range of practical problems. We propose six projects, each of which is jointly led by two or three principal investigators from different places. A dynamic and ambitious research collaboration is aspired within the whole research unit and in exchange with international experts.

由于数据的可用性不断增加，统计学在许多科学和实践领域发挥着越来越突出的作用。另一方面，最一般的现实模型通常非常复杂，因此尽管数据量很大，但统计精度很差的情况很常见。汉堡-柏林-波茨坦统计结构推理研究单位：适应和效率旨在开发新的方法和工具，以从高维复杂数据的结构中获利。结构不仅涉及未知的推理目标（涉及平滑性、稀疏性或低维），还涉及涉及未知相关矩阵、分层或多尺度交互或噪声支持属性的数据结构。长期目标是建立一个通用框架，以自动、同时适应数据中可能存在的不同结构。这将允许更有效的统计程序，这将对广泛应用中统计结果的重要性产生重大影响。此外，获得的基本见解通常可以将有效的方法快速转移到即将到来的应用中的新结构。为数学分析开发的先进新工具将推动复杂结构模型的数学统计的整个领域。该研究小组由来自汉堡大学、柏林洪堡大学、柏林维尔斯特拉研究所和波茨坦大学的八名主要研究人员组成。他们在不同统计领域的共同专业知识集中于现代有效方法，这些方法使用先进的数学理论进行分析，并适用于广泛的实际问题。我们提出了六个项目，每个项目由来自不同地方的两到三名主要研究人员共同领导。整个研究单位渴望开展充满活力和雄心勃勃的研究合作，并与国际专家进行交流。