(Joint work with Clément Berenfeld (Dauphine) and Paul Rosa (Oxford))

In high dimensions it is common to assume that the data have a lower dimensional structure. In this work we consider that the observations are iid and with a distribution whose support is concentrated near a lower dimensional manifold. Neither the manifold nor the density is known. A typical example is for noisy observations on an unknown low dimensional manifold.

We consider a family of Bayesian nonparametric density estimators based onlocation - scale Gaussian mixture priors and we study the asymptotic properties of the posterior distribution. Our work shows in particular that non conjuguate location - scale Gaussian mixture models can adapt to complex geometries and spatially varying regularity. This talk will also review the various aspects of mixture of Gaussian for density estimation.