A changepoint analysis on spatio-temporal point processes
Speaker: Linda Altieri (University of Bologna)
Changepoint analysis is a well-established area of statistical research but in the context of spatio-temporal point processes, some substantial differences have to be taken into account: firstly, at every time point the datum is an irregular pattern of points; secondly, in real situations there are issues of spatial dependence between points and temporal dependence within time segments. Our motivating example consists of data concerning the monitoring and recovery of radioactive particles from Sandside beach, North of Scotland; there have been two major changes in the equipment used to detect the particles, representing known potential changepoints. In addition, offshore particle retrieval campaigns are believed may reduce the particle intensity onshore with an unknown temporal lag. We therefore aim at detecting multiple change points in the intensity of the process.
We propose a Bayesian approach for detecting changes in the intensity of a spatio-temporal point process, allowing for spatial and temporal dependence. We use log-Gaussian Cox processes, a very flexible class of models suitable for environmental applications that can be implemented using integrated nested Laplace approximation (INLA). Once the posterior curve is obtained, we propose two methods for detecting significant change points, and we present a simulation study assessing the validity and properties of the methods.
We finally apply the above methods to the motivating dataset and find good and sensible results about the presence and quality of changes in the process.