FOR 5381: Mathematical Statistics in the Information Age - Statistical Efficiency and Computational Tractability

在信息时代，数据以及可靠和有意义的统计评估比以往任何时候都更加重要。然而，面对海量数据，统计方法面临着新的挑战。存储或隐私限制甚至需要对干净的原始数据进行预处理，其海量通常导致随后应用的经典高效统计方法的计算困难。通常，经过预处理的数据不再共享原始数据的分布属性。此外，统计上有效的数据预处理通常依赖于后续统计推断的给定任务。因此，这两个处理步骤是密不可分的。必须开发新的概念，以保证对潜在的预处理数据集的有效性和效率，同时对海量数据在计算上容易处理。我们的目标正是提供这种联合发展，从而影响现代统计数据分析的所有科学分支。在供资期间，该研究单位将成功地开发出全面的统计方法，以应对现代数据分析的这些新挑战。

In the information age, the importance of data together with reliable and meaningful statistical evaluation is greater than ever. In face of massive amounts of data, however, new challenges enter statistical methodology. Storage or privacy constraints require even clean raw data to be preprocessed, and its massiveness typically leads to computational intractability of subsequently applied classical efficient statistical methodology. Usually, preprocessed data do not share the distributional properties of the raw data any longer. Moreover, statistically efficient data preprocessing typically depends on the given task of subsequent statistical inference. Hence, both processing steps are inseparably linked. New concepts have to be developed which guarantee validity and efficiency on potentially preprocessed data sets while being computationally tractable at the same time for massive data. Our aim is to provide exactly this conjoint development, therefore influencing all scientific branches of modern statistical data analysis. Within the funding period, this research unit shall successfully develop comprehensive statistical methodology which addresses these new challenges of modern data analysis.