Modelo fatorial espaço-temporal para dados de contagem multivariados: uma aplicação aos dados de criminalidade no Estado do Rio de Janeiro

Abstract

In this work, a model called Space-Temporal Factorial Model for Multivariate Counting Data was proposed to deal with data that have multivariate, spatial, and temporal structures. In particular, area-aggregated counts data that follow the Poisson distribution were considered. In this approach, several criminal types are considered by the Integrated Areas of Public Security (AISP) of the state of Rio de Janeiro in the period from 2012 to 2020. The inference procedure was carried out under a Bayesian approach using the Monte Carlo Hamiltonian method to obtain samples from the posterior distributions of the model. For the proposed model, it is assumed that the common factors incorporate the spatial and temporal variation between observations. Studies with simulated data and real data are discussed to evaluate the model’s goodness of fit, the assumption of the number of factors, and to understand the crime phenomenon in the state.