Bayesian multivariate models for bounded directional data

In some areas of knowledge there are data representing directions restricted to a specific range of values. Consequently, it is useful to have models for describing variables defined in subsets of the k-dimensional unit sphere. This need has led to the development of models such as the multivariate projected Gamma distribution. However, the proposal of multivariate models whose marginal variables are defined only in sections of the unit circle and with a flexible dependency structure is limited. In this work, we propose an approach to constructing multivariate models where each marginal variable is a circular variable defined only in the first quadrant of the unit circle. Our approach is based on the concept of copula functions. The inferences for the proposed models rely on generating samples of the posterior joint density of all parameters involved in the models. This is achieved by applying a conditional approach that allows efficient inferences to be made using a two-stage sampling. The proposed methodology is illustrated with both simulated and real data.