  We introduce a family of multiscale stick-breaking mixture models for
Bayesian nonparametric density estimation. The Bayesian nonparametric
literature is dominated by single scale methods, exception made for P\`olya
trees and allied approaches. Our proposal is based on a mixture specification
exploiting an infinitely-deep binary tree of random weights that grows
according to a multiscale generalization of a large class of stick-breaking
processes; this multiscale stick-breaking is paired with specific stochastic
processes generating sequences of parameters that induce stochastically ordered
kernel functions. Properties of this family of multiscale stick-breaking
mixtures are described. Focusing on a Gaussian specification, a Markov Chain
Montecarlo algorithm for posterior computation is introduced. The performance
of the method is illustrated analyzing both synthetic and real data sets. The
method is well-suited for data living in $\mathbb{R}$ and is able to detect
densities with varying degree of smoothness and local features.
