GRK 1953: Statistical Modelling of Complex Systems and Processes - Advanced Nonparametric Approaches

统计领域目前正在经历剧烈的变化。在应用发展的推动下，越来越多的海量和非常复杂的数据集成为可用的(大数据)。例如气象学中快速增长的数据集，来自高频金融的数据集，其中数据以毫秒的频率被记录和分析，当然还有自动驾驶和社交网络中的新技术。这些巨大的数据集要求分析这些数据的统计方法发生变化--例如，针对维度极大的数据的新方法，或者可以在几毫秒内在线执行的金融数据的新方法。新的统计方法包括用于高维模型和降维的技术、对基础模型的结构的推断和结构性非参数建模，以及对时空数据、随机网络和金融数据的依赖关系的灵活建模。这个研究培训小组(RTG)将致力于复杂随机系统和过程的高级非参数统计建模领域的基础研究。在这里，基础研究既意味着新方法的开发，也意味着对新方法的数学调查，这对于彻底理解复杂的情况是必不可少的。目前在这一领域的工作利用了概率论和数理统计方面的深入理论发展。因此，对现代概率和数理统计有广泛的了解是必要的。RTG的主要目的是为年轻的博士研究人员提供先进的数学基础，并为他们在现代理论统计前沿的研究提供国际联系。

The field of statistics is currently undergoing drastic change. Driven by the development in applications, more and more massive and very complex data sets have become available ("big data"). Examples are the fast-growing data sets in meteorology, the data sets from high-frequency finance where data are recorded and analyzed at the frequency of a millisecond, and of course new technologies in autonomous driving and social networks. These huge data sets require a change in statistical methods for analyzing such data – for example new methods for data whose dimension is extremely large, or new methods for financial data which can be performed online in milliseconds. The new statistical methodology includes techniques for high-dimensional models and dimension reduction, inference on the structure of underlying models and structural nonparametric modeling, and flexible modeling of dependencies for spatio-temporal data, stochastic networks and financial data. This research training group (RTG) will be devoted to fundamental research in the area of advanced nonparametric statistical modeling of complex stochastic systems and processes. Here, fundamental research means both the development and the mathematical investigation of new methodologies, which is essential for a thorough understanding of complex situations. Current work in this area makes use of deep theoretical developments in probability theory and mathematical statistics. Therefore, a broad knowledge of modern strands of probability and mathematical statistics is necessary. The main intention of the RTG is to offer young doctoral researchers an advanced mathematical basis and international contacts for their research at the frontier of modern theoretical statistics.