Inference for Dependent Data
Many data are recorded from large and complex dependent processes, with dependence due for example to time, space and/or structured measurement (as in experimental design). We contribute to the development of data analytics methods for time series, random fields (spatial statistics), longitudinal and repeated measurements data (latent variable models), with applications in signal processing for navigation, population health, psychological and educational sciences.
Extracting information from complex data, with huge number of features (high dimensional settings) is currently one of the most important challenge for data analytics. On the one side, new statistical methods, valid in high dimensions (conceptually, dimensions that can be infinite), need to be developed and, on the other side, these methods should be computable in practice within the limits of available computer performances. We contribute to the development of computationally efficient statistical methods for estimation, inference and model selection in high dimensions, with applications to medical sciences.
Data analysis is part of the scientific process, as it can be used to validate/invalidate scientific hypotheses and/or to predict expected outcomes given a model. The later can be more or less flexible and/or general, but is always based on a (minimal) set of assumptions. With the availability of huge amounts of data, deviations from these assumptions (model deviations), such as so-called outliers, often occur in observed data sets. Robust statistics provides a theoretical framework for estimation and inference techniques that are less sensitive to (any type of) model deviations. We contribute to the development of robust methods for time series and spatial statistics analysis, model selection and (flexible) multivariate modelling (copulas), with applications to economics, behavioral sciences, signal processing.
Life sciences analytics
The ever-growing amount of available data, as issued from biological and/or genetic measurements or as features from medical images, allow life sciences researchers to breach the frontiers of knowledge in many directions, outside the controlled experimental settings. Data analytics, in this context, consists in using and developing statistical methods that can control population (or out-of-sample) validity (e.g. under sampling bias, measurement error, etc.), by controlling the decisional risk associated to hypothesis testing and/or prediction. We contribute to the application and development of new data analytics methods, in high dimensions, for estimation, prediction and/or model selection.
Data Analytics in Engineering
The analysis of data when studying or improving existing technologies as well as developing new procedures and mechanisms is a core and cross-cutting task over the different fields of engineering. Understanding if and how different solutions perform in different settings is essential to ensure that research in engineering delivers reliable results and this is often based on complex experimental settings which deliver challenges when trying to analyse and interpret the corresponding data. Hence, for example, new signal processing or feature selection tools are necessary to extract information from these complex data settings.
Statistical analysis can be used within a wide range of settings but often researchers and practitioners are faced with very specific problems for which no suitable statistical method is adapted to a particular data set. Our research also focuses on adapting and/or creating new methodologies tailored to the problem at hand for providing decisional frameworks with controlled decisional risk. Examples include business analytics, media analytics, life sciences analytics.