For the purpose of nonparametric density estimation, a prior distribution is constructed on the space of stepwise constant density functions, not necessarily of bounded support. In particular, the sequence of heights is conditionally distributed a priorias a Dirichlet process on the integers, given a bidimensional mixing parameter. Such a mixing parameter is composed of a bin width and a starting point which are, in turn, assigned an arbitrary marginal prior.

Proper Bayesian estimates of the density are obtained. They are not histograms, but they share common features with the histogram and other kernel based estimators. They also incorporate prior information, like a prior guess for the density or bounds for its support, which may be particularly appealing for small sample situations, where usual density estimation methods are not satisfactory.

The estimates are computable by simple numerical methods, as opposed to other nonparametric Bayesian density estimators proposed in the literature, which display significant computational problems. Moreover, a simple way to generate density functions from the posterior process allows for simulation of Bayesian intervals for functionals of the density, in particular for the density itself at fixed points.