Loosely speaking, a point process is a stochastic process that scatters points in space and/or time. Typical examples include the mapped positions of trees in a forest, the times of incoming calls at a help desk, or the list of times and epicentres of earthquake occurrences.
This project (NWO Open Competition, (OCENW.KLEIN.068)) is motivated by studies into property crimes such as bicycle thefts and domestic burglaries. For example, when victims report a burglary, the location is usually known but the time of the break-in may well be censored because of the absence of the occupants. Reconstruction of such missing information based on the available data is known as ‘state estimation’ and includes the extrapolation of a spatial or temporal pattern beyond the window of observation. The overall goal is to develop a spatio-temporal point process model and propose tools for state estimation that can be used to identify areas and time slots at increased risk. This enables the authorities to use resources, such as patrol capacity, intelligently and to launch public awareness campaigns where and when they are most needed.
Results
M.N.M. van Lieshout and R.L. Markwitz. State estimation for aoristic models. Scandinavian Journal of Statistics 50:1068--1089, 2023.
M.N.M. van Lieshout and R.L. Markwitz. A non-homogeneous semi-Markov model for interval censoring. ArXiv 2401.17905, January 2024.
R.L. Markwitz. A likelihood-based approach to modelling aoristic crime data. To appear in: Proceedings of "Criminal Justice and Security in Central and Eastern Europe 2023".