Date of Award
Fall 2022
Document Type
Thesis
Degree Name
Master of Science (MS) in Mathematics
Department
Mathematical, Computing & Information Sciences
Committee Chair
Dr. Jason Cleveland
Abstract
In this paper we explore Bayesian inference and its application to the problem of estimating the intensity function of a non-homogeneous Poisson process. These processes model the behavior of phenomena in which one or more events, known as arrivals, occur independently of one another over a certain period of time. We are concerned with the number of events occurring during particular time intervals across several realizations of the process. We show that given sufficient data, we are able to construct a piecewise-constant function which accurately estimates the mean rates on particular intervals. Further, we show that as we reduce these intervals in size, at the limit we are able to reconstruct the original intensity function.