Math @ Duke

Publications [#329118] of David B. Dunson
search arxiv.org.Papers Published
 Canale, A; Dunson, DB, Multiscale bernstein polynomials for densities,
Statistica Sinica, vol. 26 no. 3
(July, 2016),
pp. 11751195, Institute of Statistical Science [doi]
(last updated on 2019/05/19)
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 overlyspiky 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 infinitelydeep binary tree, we place a beta dictionary density; within a scale the densities are equivalent to Bernstein polynomials. Using a stickbreaking 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 locallyvarying 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.


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