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Prior specification for nonparametric Bayesian inference involves thedifficult task of quantifying prior knowledge about a parameter of high, ofteninfinite, dimension. Realistically, a statistician is unlikely to have informedopinions about all aspects of such a parameter, but may have real informationabout functionals of the parameter, such the population mean or variance. Thisarticle proposes a new framework for nonparametric Bayes inference in which theprior distribution for a possibly infinite-dimensional parameter is decomposedinto two parts: an informative prior on a finite set of functionals, and anonparametric conditional prior for the parameter given the functionals. Suchpriors can be easily constructed from standard nonparametric priordistributions in common use, and inherit the large support of the standardpriors upon which they are based. Additionally, posterior approximations underthese informative priors can generally be made via minor adjustments toexisting Markov chain approximation algorithms for standard nonparametric priordistributions. We illustrate the use of such priors in the context ofmultivariate density estimation using Dirichlet process mixture models, and inthe modeling of high-dimensional sparse contingency tables.

Marginally Specified Priors for Nonparametric Bayesian Estimation