  We introduce a density basis of the trigonometric polynomials that is
suitable to mixture modelling. Statistical and geometric properties are
derived, suggesting it as a circular analogue to the Bernstein polynomial
densities. Nonparametric priors are constructed using this basis and a
simulation study shows that the use of the resulting Bayes estimator may
provide gains over comparable circular density estimators previously suggested
in the literature. From a theoretical point of view, we propose a general prior
specification framework for density estimation on compact metric space using
sieve priors. This is tailored to density bases such as the one considered
herein and may also be used to exploit their particular shape-preserving
properties. Furthermore, strong posterior consistency is shown to hold under
notably weak regularity assumptions and adaptative convergence rates are
obtained in terms of the approximation properties of positive linear operators
generating our models.
