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.