We deal with recurrent event processes, where occurrence and timing of certain events are recorded. We specify a general model for the hazard function of the related counting process, which is allowed to depend on (i) time (both in a parametric and non-parametric fashion), (ii) observed covariates, (iii) unobserved covariates, and (iv) past events for the same subject. A discrete latent variable, which is allowed to evolve over time according to a continuous-time homogeneous Markov chain, captures unobserved heterogeneity. Past events can transiently increase (self-excitation, as in Hawkes processes) or decrease (self-correction) the hazard of future events.
We derive inference both in a classical and Bayesian framework. We also discuss the relevant case of biased sampling, where only units with at least one event can be recorded. We link this case with the problem of continuous-time population size estimation. We illustrate with two examples. First, an application to terrorist attacks in n=30 European countries in the period 2001–2017, where we find two distinct latent clusters, negative association with GDP growth, and self-exciting phenomena. Secondly, a sample of n=4271 Italian drug dealers, who were identified at least once by the Italian police in a period of two years, which lead us to identify self-correcting phenomena and estimate a population of about 90000 illicit drug dealers active in the period.
Zoom link: https://uoc-gr.zoom.us/j/88659969718?pwd=g6bjYPDCuUQo1bzVxjjbgQL4xFN1f3.1
