Multiscale stick-breaking mixture models

Abstract Bayesian nonparametric density estimation is dominated by single-scale methods, typically exploiting mixture model specifications, exception made for Pólya trees prior and allied approaches. In this paper we focus on developing a novel family of multiscale stick-breaking models that inherits some the advantages both mixtures trees. Our proposal based specification an infinitely deep binary tree random weights grows according to generalization large class processes; paired with specific stochastic processes generating sequences parameters induce stochastically ordered kernel functions. Properties are described. Focusing Gaussian specification, Markov Chain Monte Carlo algorithm posterior computation introduced. The performance method illustrated analyzing synthetic real datasets consistently showing competitive results in scenarios favoring methods. suggest well suited estimate densities varying degree smoothness local features.