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Multivariate Heavy Tail Phenomena: Modeling and Diagnostics

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Project Summary

This project aims to develop reliable diagnostic, inferential and model validation tools for heavy tailed multivariate data; to generate new classes of multivariate heavy tailed models that highlight the implications of dependence and tail weight; and to apply these statistical and mathematical developments to the key application areas of network design and control, social network analysis, and signal processing. Our application interests also include network security, anomaly detection, and risk analysis.

In order to understand and exploit multivariate heavy tail phenomena in DOD application areas of interest, our project will develop statistical, mathematical and software tools that provide:

  • Flexible and practical representations of multidimensional heavy tail distributions that permit reliable statistical analysis and inference; allow model discovery, selection and confirmation; quantify dependence; and overcome the curse of dimensionality.
  • Heavy tailed mathematical models that can be calibrated; which clearly exhibit the influence of dependence and tail weight; and which are appropriate to the applied context.
  • Exploitation of the new tools of multivariate heavy tail analysis to study social networks, packet switched networks, network design and control, and robust signal processing.

Our team possesses broad and complementary expertise in mathematics, statistics, computing, engineering and technology transfer.