Abstract
Directional data appears in several branches of research. In some cases, those directional variables are only defined in subsets of the K-dimensional unit sphere. For example, in some applications, angles as measured responses are limited on the positive orthant. Analysis on subsets of the K-dimensional unit sphere is challenging and nowadays there are not many proposals that discuss this topic. Thus, from a methodological point of view, it is important to have probability distributions defined on bounded subsets of the K-dimensional unit sphere. Specifically, in this paper, we introduce a nonparametric Bayesian model to describe directional variables restricted to the first orthant. This model is based on a Dirichlet process mixture model with multivariate projected Gamma densities as kernel distributions. We show how to carry out inference for the proposed model based on a slice sampling scheme. The proposed methodology is illustrated using simulated data sets as well as a real data set.