Printed in Great Britain Bayesian curve fitting using multivariate normal mixtures

Problems of regression smoothing and curve fitting are addressed via predictive infer-ence in a flexible class of mixture models. Multidimensional density estimation using Dirichlet mixture models provides the theoretical basis for semi-parametric regression methods in which fitted regression functions may be deduced as means of conditional predictive distributions. These Bayesian regression functions have features similar to gener-alised kernel regression estimates, but the formal analysis addresses problems of multivari-ate smoothing, parameter estimation, and the assessment of uncertainties about regression functions naturally. Computations are based on multidimensional versions of existing Markov chain simulation analysis of univariate Dirichlet mixture models. Some key words: Bayesian regression estimation; Dirichlet mixture model; Markov chain simulation; Multivariate density estimation; Smoothing. 1