Statistical methods for point-process time series

University Of Wisconsin-Milwaukee, Milwaukee WI

Investigators

Abstract

This research project will develop statistical models and inference methods for the analysis of random point processes. Random point processes are events that occur at random in time or space according to certain patterns; this project will provide methods for the discovery and analysis of such patterns. Examples of events that can be modelled as random point processes include cyberattacks on a computer network, earthquakes, crimes in a city, spikes of neural activity in humans and animals, car crashes in a highway, and many others. Therefore, the methods to be developed under this project will find applications in many fields, such as national security, economy, neuroscience and geosciences, among others. The project will also provide training opportunities for graduate and undergraduate students in the field of Data Science. This project will specifically develop statistical tools for the analysis of time series of point processes, that is, for point processes that are observed repeatedly over time; for example, when the spatial distribution of crime in a city is observed for several days. These tools will include trend estimation methods, autocorrelation estimation methods, and autoregressive models. Research activities in this project include the development of parameter estimation procedures, their implementation in computer programs, the study of theoretical large sample properties of these methods, the study of small sample properties by simulation, and their application to real-data problems. Other activities in this project include educational activities, such as the supervision of Ph.D. and Master's students, and the development of graduate and undergraduate courses in Statistics and Data Science. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.