Estimando modelos dinâmicos utilizando o INLA para campos aleatórios Markovianos não gaussianos

Abstract

State-space models, also referred as Dynamic Models, is a useful way to describe the evolution of a time series variable through a structured latent evolution system. Integrated Nested Laplace Approximation (INLA) is a recent approach proposed to perform fast Bayesian inference in Latent Gaussian Models which naturally comprises Dynamic Models. Originally, the INLA approach is retricted to perform estimates where the Latent Field is assumed to be Gaussian distributed, which make not possible the estimation of Dynamic Models assuming a non-Gaussian distribution for the latent system noise. The objective of this work is to describe the INLA methodology, Dynamic Models, and how to overcome this issue presenting a way to use INLA for Robust Dynamic Models assuming a Student-t Random Field. Simulations under several scenarios were conducted highlighting the importance of this robust approach when time series present what is called in the literature as Innovative Outliers. At last, two application were conducted exemplifying the presented models; the first application is on annual homicide data of brazilian cities and the second on monthly data of dengue fever of the brazilian state of Minas Gerais.