Marginally specified priors for non-parametric Bayesian estimation.

Published

Journal Article

Prior specification for non-parametric 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 non-parametric 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 non-parametric conditional prior for the parameter given the functionals. Such priors can be easily constructed from standard non-parametric 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 non-parametric 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.

Full Text

Duke Authors

Cited Authors

  • Kessler, DC; Hoff, PD; Dunson, DB

Published Date

  • January 2015

Published In

Volume / Issue

  • 77 / 1

Start / End Page

  • 35 - 58

PubMed ID

  • 25663813

Pubmed Central ID

  • 25663813

International Standard Serial Number (ISSN)

  • 1369-7412

Digital Object Identifier (DOI)

  • 10.1111/rssb.12059

Language

  • eng