Multiscale bernstein polynomials for densities

Journal Article (Journal Article)

Our focus is on constructing a multiscale nonparametric prior for densities. The Bayes density estimation literature is dominated by single scale methods, with the exception of Polya trees, which favor overly-spiky densities even when the truth is smooth. We propose a multiscale Bernstein polynomial family of priors, which produce smooth realizations that do not rely on hard partitioning of the support. At each level in an infinitely-deep binary tree, we place a beta dictionary density; within a scale the densities are equivalent to Bernstein polynomials. Using a stick-breaking characterization, stochastically decreasing weights are allocated to the finer scale dictionary elements. A slice sampler is used for posterior computation, and properties are described. The method characterizes densities with locally-varying smoothness, and can produce a sequence of coarse to fine density estimates. An extension for Bayesian testing of group differences is introduced and applied to DNA methylation array data.

Full Text

Duke Authors

Cited Authors

  • Canale, A; Dunson, DB

Published Date

  • July 1, 2016

Published In

Volume / Issue

  • 26 / 3

Start / End Page

  • 1175 - 1195

International Standard Serial Number (ISSN)

  • 1017-0405

Digital Object Identifier (DOI)

  • 10.5705/ss.202015.0163

Citation Source

  • Scopus