Bayesian multiscale mixture of Gaussian kernels for density estimation

In this paper we discuss some preliminary results related to a novel Bayesian nonparametric method for multiscale density estimation. Specifically, we extend the model by [1]—originally developed for compact sample spaces—to deal with data taking values in the whole real line R. By means of an infinitely-deep binary tree of kernels, we are able to construct a multiscale mixture model able to approximate densities with varying degrees of smoothness and local features. Sampling from the posterior distribution is available with a Markov Chain Monte Carlo method.