A. I. Escudero Villa, J. Mateu, J. M. Angulo

Crime is a negative phenomenon that affects every country in the world. Crime usually comes in form of spatio-temporal coordinates, and thus spatio-temporal point process models are good mathematical tools to analyse this type of data. We here analyse the spatio-temporal distribution of criminal acts in the city of Riobamba-Ecuador. We used a log-Gaussian Cox Process model using MCMC and MALA for inference, and a combination of glm and gam with b-splines whit covariates to model the temporal and spatial components. As an alternative model, we used a Hawkes point process to identify the self-exiting mechanisms between the series of crimes in a continuous time. We estimated the background rate of each component with non-parametric stochastic reconstruction. We obtained two relaxation coefficients to stabilize and secure the estimation process, and used semiparametric maximum likelihood.

Keywords: Bayesian inference, B-splines, Hawkes point processes, log-Gaussian Cox processes, spatio-temporal processes


Spatial Statistics and Temporal Space II
June 7, 2022  4:50 PM
Conference hall

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