Robust methods for complex data

私营和上市公司、各级政府、公共政策制定者甚至非政府组织目前都充斥着数据，并且面临着越来越大的有效利用数据的压力。理解所有可用信息是一项持续的严峻挑战，而统计在将不断涌入的数据转化为有用信息方面发挥着基础作用。这些数据的很大一部分是在没有遵循既定实验方案的情况下收集的。因此，用户面临着数据可能无法代表单一明确定义群体的难题。这意味着分析这些数据的结果可能会有偏差，因为所提出的模型可能不适用于所有观察结果。为了基于此类异构数据集执行可靠且信息丰富的推理，我们需要能够将模型拟合到数据的主要同质子集（并识别其模式）的统计方法，而不受结构上不同的较小子组的影响。稳健统计正是这样做的。我计划开发新的稳健的统计方法，可应用于目前在许多科学学科中占主导地位的大型复杂数据集。例如，考虑通过安装在海洋哺乳动物身上的标签收集的数据。这些数据集通常很大、很复杂（高频，有些数据，如 3D 加速，是间接观察到的）并且有噪声（例如来自 Argos 卫星标签的位置）。这些数据是由有兴趣了解动物的运动和行为并确定其栖息地的科学家收集的。这些问题和数据提出了具有挑战性的统计问题。例如，标记动物的运动可能会受到正在测量的变量的影响，从而导致观察结果并不构成通常理解的随机样本。此外，这些数据包含虚假或错误点（卫星链路不良或其他偶发的设备故障）的情况并不少见。此类数据是在类似情况下收集的（例如从智能手机上的传感器收集的个性化环境信息），因此我的研究将适用于各种不同的情况。**

Private and public companies, all levels of government, public policy makers, and even NGO's are currently awash with data, and under increasing pressure to utilize it efficiently. Making sense of all the available information is an ongoing critical challenge, and Statistics has a fundamental role to play in translating this growing influx of data into useful information. A large proportion of these data are being collected without following established experimental protocols. As a result, users face the difficult problem of having data that may not represent a single well-defined population. This means that the results of analyzing these data may be biased because the proposed models might not apply to all the observations. To perform reliable and informative inference based on such heterogeneous data sets, we need statistical methods that can fit models to (and identify patterns on) a dominant homogeneous subset of the data without being affected by structurally different smaller subgroups of them. Robust Statistics does exactly this. I plan to develop new robust statistical methods that can be applied to the large and complex data sets that are currently predominant in many scientific disciplines. Consider, for example, data collected by tags mounted on marine mammals. These data sets are typically large, complex (high frequency, some, like 3D acceleration, observed indirectly) and noisy (e.g. location from Argos satellite tags). These data are collected by scientists interested in understanding the animals' movement and behavior, and determining their habitat. These questions and data raise challenging statistical problems. For example, the movement of the tagged animals may be influenced by the variables being measured, in such a way that the resulting observations do not constitute a random sample as it is usually understood. Furthermore, it is not uncommon for these data to contain spurious or erroneous points (poor satellite links or other sporadic equipment failures). This type of data are being collected in similar situations (e.g. personalized environmental information collected from sensors on smartphones), so my research will be applicable to a variety of different situations.**