  A Bayesian nonparametric method for unimodal densities on the real line is
provided by considering a class of species sampling mixture models containing
random densities that are unimodal and not necessarily symmetric. This class of
densities generalize the model considered by Brunner (1992, Statist. Probab.
Lett.), in which the Dirichlet process is replaced by a more general class of
species sampling models. A novel and explicit characterization of the posterior
distribution via a finite mixture of two dependent $\mathbf{S}$-paths is
derived. This results in a closed-form and tractable Bayes estimator for any
unimodal density in terms of a finite sum over two $\mathbf{S}$-paths. To
approximate this class of estimates, we propose a sequential importance
sampling algorithm that exploits the idea of the accelerated path sampler, an
efficient path-sampling Markov chain Monte Carlo method. Numerical simulations
are given to demonstrate the practicality and the effectiveness of our
methodology.
