Develop statistical software to understand the structure of dependent events
Improve sensor design and interpretation of data
Very rarely are events that occur in sequence, whether they're hard drive failures in storage systems, component failures in a mechanical device or network, or even events in a time series, actually independent. The notion of autocorrelation has been employed to discuss the effects past events have on current ones. The problem is that autocorrelation is a linear measure, with no information as to any underlying structure of the event interactions. That is, we can only tell that events are autocorrelated and by what magnitude, but we can't say much about how they depend on one another.
The Math Citadel has done extensive work developing the formal notion of dependency theory among sequences of random variables, extending this idea to autocorrelation. This research would extend these recent developments to the statistical notion of autocorrelation, giving a more complete framework for understanding the "how" of dependent events, rather that simply just identifying that the events are dependent.
"Cascading failures" is a notion that failures have effects on future issues. This research would aid in the understanding of how cascading failures in a variety of areas such as networking, storage, and manufacturing arise.
Understanding how a time series is autocorrelated, rather than just the magnitude and lag of autocorrelation can lead to better time series modeling and predictive ability.
Arrivals to a server, router, cash register, or retail establishment may be autocorrelated, especially at micro level. Developing a framework to study the underlying structure of batch or clumped arrivals can aid in improved capacity planning