Bayesian density estimation using Bernstein polynomials

We propose a Bayesian nonparametric procedure for density estimation, for data in a closed, bounded interval, say [0, 1]. To this aim, we use a prior based on Bernstein polynomials. This corresponds to expressing the density of the data as a mixture of given beta densities, with random weights and a random number of components. The density estimate is then obtained as the corresponding predictive density function. Comparison with classical and Bayesian kernel estimates is provided. The proposed procedure is illustrated in an example; an MCMC algorithm for approximating the estimate is also discussed.