Speaker: Rosario Barone – University of Rome “Tor Vergata”

Title: Bayesian time-interaction point process

Abstract:

In the temporal point process framework, behavioral effects correspond to conditional dependence of event rates on times of previous events. This can result in self-exciting processes, where the occurrence of an event at a time point increases the probability of occurrence of a later event, or in self-correcting processes, where the occurrence of an event at a time point decreases the probability of occurrence of a later event. Altieri et al. (2022) defined as time-interaction process a temporal point processes that is the combination of self-exciting and self-correcting point processes, allowing each event to increase and/or decrease the likelihood of future ones. From the Bayesian perspective, we generalize the existing model in several directions: we account for covariates and propose a nonparametric baseline, which guarantees more flexibility and allows to control for heterogeneity. Also, we let the model parameters be modulated by a discrete state continuous time latent Markov process. Posterior inference is performed via efficient Markov chain Monte Carlo (MCMC) sampling, avoiding the implementation of discretization methods like Forward-Backward or Viterbi algorithm. Indeed, by extending Hobolth and Stone (2009), we propose a data augmentation approach that allows to simulate the continuous time latent Markov trajectories. We present applications to simulated and terrorist attacks data.

REFERENCES Altieri, L., Farcomeni, A., and Fegatelli, D. A. (2022). Continuous timeinteraction processes for population size estimation, with an application to drug dealing in Italy. Biometrics. Hobolth, A. and Stone, E. A. (2009). Simulation from endpoint-conditioned, continuous-time Markov chains on a finite state space, with applications to molecular evolution. The Annals of Applied Statistics, 3(3): 1204-1231.