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

由于数据的日益可获得性，统计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，但统计精度很低的情况很常见。汉堡-柏林-波茨坦研究单位统计中的结构推断：适应和效率旨在开发新的方法和工具，以便从高维复杂数据背后的结构中获利。结构不仅涉及未知的推理目标(涉及光滑性、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支持特性的噪声的数据结构。长期目标是建立一个总框架，以便自动和同时适应数据中可能出现的不同结构。这将大大提高统计程序的效率，这将对统计结果在广泛应用中的重要性产生重大影响。此外，获得的基本洞察力通常将允许在即将到来的应用中快速将有效的方法转移到新的结构中。为数学分析开发的先进的新工具将推动复杂结构模型的整个数理统计领域。研究单位由来自汉堡大学、柏林洪堡大学、柏林魏尔斯特拉研究所和波茨坦大学的8名首席研究员组成。他们在不同统计领域的联合专门知识集中在现代有效方法上，这些方法使用先进的数学理论进行分析，适用于广泛的实际问题。我们提出了六个项目，每个项目都由两到三个来自不同地方的首席调查人员共同领导。在整个研究单位内，并与国际专家交流，渴望有一个充满活力和雄心勃勃的研究合作。

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.