Bayes prediction density and regression estimation - A semiparametric approach

This paper is concerned with the Bayes estimation of an arbitrary multivariate density, f(x), x ∃ R^k. Such an f(x) may be represented as a mixture of a given parametric family of densities {h (x|θ)} with support in R^k, where θ (in R^d) is chosen according to a mixing distribution G. We consider the semiparametric Bayes approach in which G, in turn, is chosen according to a Dirichlet process prior with given parameter α. We then specialize these results when f is expressed as a mixture of multivariate normal densities Φ (x|Μ, λ) where Μ is the mean vector and λ is the precision matrix. The results are finally applied to estimating a regression parameter.