Robust methods for complex data

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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.