Math @ Duke

Publications [#257849] of David B. Dunson
search arxiv.org.Papers Published
 Kessler, DC; Hoff, PD; Dunson, DB, Marginally specified priors for nonparametric Bayesian estimation.,
Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol. 77 no. 1
(January, 2015),
pp. 3558, ISSN 13697412 [doi]
(last updated on 2019/05/19)
Abstract: Prior specification for nonparametric Bayesian inference involves the difficult task of quantifying prior knowledge about a parameter of high, often infinite, dimension. A statistician is unlikely to have informed opinions about all aspects of such a parameter but will have real information about functionals of the parameter, such as the population mean or variance. The paper proposes a new framework for nonparametric Bayes inference in which the prior distribution for a possibly infinite dimensional parameter is decomposed into two parts: an informative prior on a finite set of functionals, and a nonparametric conditional prior for the parameter given the functionals. Such priors can be easily constructed from standard nonparametric prior distributions in common use and inherit the large support of the standard priors on which they are based. Additionally, posterior approximations under these informative priors can generally be made via minor adjustments to existing Markov chain approximation algorithms for standard nonparametric prior distributions. We illustrate the use of such priors in the context of multivariate density estimation using Dirichlet process mixture models, and in the modelling of high dimensional sparse contingency tables.


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