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Bayesian curve fitting using multivariate normal mixtures. (English) Zbl 0865.62029

Summary: Problems of regression smoothing and curve fitting are addressed via predictive inference 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 generalized kernel regression estimates, but the formal analysis addresses problems of multivariate 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.

MSC:

62G07 Density estimation
62F15 Bayesian inference
62H12 Estimation in multivariate analysis
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