Modelos multivariados espaço-temporais com covariâncias variando no tempo

Abstract

Recently, multivariate space-time models have attracted the interest of many researchers for data modeling because they accommodate complex dependency structures, being applied in several areas such as environmental sciences, ecology, epidemiology, among others. These models attempt to describe the existent relationship in a process considering the dependency between the variables, in different locations and through time. In many cases, the application of such models is difficult due to the high computational cost involved in their implementation and the need to specify cross-covariances, which can be challenging. To deal with it, a conditional approach was considered to define a multivariate Gaussian process. A conditional approach was considered to specify a multivariate Gaussian process. This approach specifies a joint distribution of a spatial process through a product of conditionals. Sparsity can be obtained in the correlation matrix by limiting the number of conditioning in each factor. In this work, a mixture model was proposed, it includes models specified under different organizations of conditioning variables. Also, it was considered a model selection method based on predictive distribution to obtain a smaller subset and limitate the number of components in the mixture. In this model, the mixture weights evolve through time following a Dirichlet process, resulting in flexibility in the dependency structure between the variables, allowing this to vary through time. Simulated studies with different scenarios of interest are presented and illustrate the flexibility of the proposed model. Furthermore, an application on air pollution data was performed.