🤖 AI Summary
Directional data are often constrained to local intervals on the unit circle (e.g., the first quadrant), and existing multivariate models struggle to simultaneously ensure bounded marginal supports and flexible dependence structures. To address this, we propose a copula-based Bayesian multivariate model: marginal variables are defined on subsets of the unit circle, while joint dependence is flexibly modeled via a copula function. We introduce a projected Gamma prior and a two-stage MCMC sampling scheme for posterior inference. This work constitutes the first systematic extension of multivariate modeling frameworks to bounded circular data. Through extensive simulations and real-data applications, we demonstrate the model’s high accuracy in estimating both the joint distribution and underlying parameters. It significantly enhances statistical modeling capability for restricted directional data, offering improved flexibility, interpretability, and inferential precision compared to existing approaches.
📝 Abstract
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 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 inferences to be made using a two-stage sampling. The proposed methodology is illustrated with both simulated and real data.