Spatio-temporal point process models for interval-censored data
Robin Markwitz is a PhD student in the department Mathematics of Operations Research. (Co)Promotors are prof.dr.M.N.M. van Lieshout and prof.dr. R.J. Boucherie from the faculty of Electrical Engineering, Mathematics and Computer Science, University of Twente.
In this thesis, we develop a number of statistical frameworks within which interval-censored data can be modelled. By interval-censored data, we refer to data in which events can be partially observed in the form of temporal intervals, instead of being fully observed as simply a point in time and space. The base statistical model consists of two separate stochastic processes. One is responsible for the interval censoring mechanism, whereas the other process is a point process modelling the behaviour of the underlying stochastic process responsible for the event times. We blend approaches from stochastic processes, point process theory and measure theory to develop rigorous theoretical and modelling frameworks for temporal data. The spatial location of a point may also play a significant role in modelling, and in many cases, the geometry of the spatial component of the data is quite complex. We extend the underlying point process to take values on Euclidean graphs, and develop robust simulation and parameter estimation methods for this complex spatio-temporal model. The developed statistical theory has significant potential to be applied in the field of criminology, as both burglaries and arson fires are often only partially observed and recorded by victims and law enforcement. Models developed in this thesis are applied to a number of simulated and real-life data sets, with the full spatio-temporal model being applied to a car arson fire data set in Enschede.
