Latent Markov time-interaction processes

We present parametric and semiparametric latent Markov time-interaction processes, that are point processes where the occurrence of an event can increase or reduce the probability of future events. We first present time-interaction processes with parametric and nonparametric baselines, then we let model parameters be modulated by a discrete state continuous time latent Markov process. Posterior inference is based on a novel and efficient data augmentation approach in the Markov chain Monte Carlo framework. We illustrate with a simulation study; and an original application to terrorist attacks in Europe in the period 2001–2017, where we find two distinct latent clusters for the hazard of occurrence of terrorist events, negative association with GDP growth, and self-exciting phenomena. Supplementary materials for this article are available online.