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 anf(x) may be represented as a mixture of a given parametric family of densities {h (x¦θ)} with support inR ^k, whereθ (inR ^d) is chosen according to a mixing distributionG. We consider the semiparametric Bayes approach in whichG, in turn, is chosen according to a Dirichlet process prior with given parameterα. We then specialize these results whenf is expressed as a mixture of multivariate normal densitiesΦ (x¦Μ, λ) whereΜ is the mean vector and λ is the precision matrix. The results are finally applied to estimating a regression parameter.