“Multivariate statistical signal modeling and analysis”. Patrice Abry, Herwig Wendt.

The massive deployment of sensors for monitoring systems has recently led, in an increasing number of applications of various natures (e.g., biomedical, geophysics, climatology, econometrics, computer and telecommunication networks), to large size collections of data that are naturally multivariate, with a massive number of components. The focus is therefore shifting from the modeling and analysis of individual time series or images to the modeling and inference of the information that is jointly conveyed by the collection of data components, as well as of dependencies and causalities. The growing importance of the topic is reflected by the recent organization of several special sessions and invited lectures at international conferences (e.g., IEEE Symposium on Computational Intelligence and Data Mining 2014, Symposium of the Society for Nonlinear Dynamics and Econometrics 2015, IEEE World Congress in Computational Intelligence 2016, Biosignals 2016), most of which are dedicated to specific applications.

The increasingly large-scale nature of multivariate data is stimulating new developments in the classical topic of multivariate statistical analysis. Notably, many traditional analysis and inference methodologies, designed for univariate time series, have been found to be of limited relevance when confronted with large-scale multivariate data. This has generated much interest in the development of novel, intrinsically multivariate statistical tools, stemming from many different sub-domains of statistics and data analysis and including, for instance, probabilistic graphical models or explicit modeling of dependence via, e.g., copula. These numerous recent contributions to multivariate signal analysis are, however, scattered in the literature dedicated either to specific application domains or categories of tools or subfields of statistics and data analysis.

We thus believe that there is a significant need to assemble and confront with each other such recent developments. The objective of this special session is hence to present several methodological contributions dedicated to multivariate statistical signal modeling and analysis, different in spirit or nature. This includes contributions dedicated to multi-correlation assessment, to graph-based versus network-based approaches, to time-evolving multi-correlation structures, to multivariate linear modeling, to Bayesian inference in multivariate convex inverse problems, to data adaptive metrics for causality assessment, to multivariate scale-free modeling and testing. Furthermore, though the focus of this special session is on methodological and theoretical developments, their use in real-world applications (e.g., macro-brain analysis, econometric modeling) will also be illustrated.