Publications [#329118] of David B. Dunson

Papers Published

1. Canale, A; Dunson, DB, Multiscale bernstein polynomials for densities, Statistica Sinica, vol. 26 no. 3 (July, 2016), pp. 1175-1195, Institute of Statistical Science [doi]
   (last updated on 2025/04/11)

   Abstract:
   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.