Title:  Maximum Likelyhood Estimation of Poisson and Hawkes Processes and Extensions to Hawkes Process Analysis

Committee: 

Dr. Davenport, Advisor

Dr. Rozell, Chair

Dr. Song

Abstract:

The objective of the proposed research is to improve our ability to extract information from data generated by Hawkes processes. To this end, we will begin with recovery bounds for linear Poisson processes. Existing results only apply to Poisson counting processes, but we will develop a new result that holds for arrival processes, which are more general. While we mainly treat this as an intermediate result, it has implications across the wide array of problems involving Poisson processes and other forms of point processes. In our second aim, we will explore the implications for one point process in particular. Specifically, we will seek to provide an answer to the question ``How well can we recover the parameters that govern Hawkes processes?" No existing results address this question. In our final aim, we will explore several ways that the Hawkes model can be used to provide insight into a system beyond the face-value of the learned parameters.