Bayesian Kernel Density Estimation
Dec 31 1989
Bayesian estimation of density and distribution functions is developed using models based on mixtures of Dirichlet processes. The complicated structure of posterior and predictive distributions in such process models is described, as are various suggestion for their approximation. One particular method of approximation, leading to Bayesian analogues of (standard, non-Bayesian and non-model based) kernel density techniques, is described and illustrated. This shows how variations of kernel techniques have approximate model based foundation, with subsequent implications for extensions and modifications based foundation, with subsequent implications for extensions and modifications based on variations in the underlying model. Alternative approaches to approximate inference in Dirichlet mixture models are also introduced, putting the basic kernel type technique clearly into perspective, and some of the practicalities of data analysis using such approximations are discussed, with illustration. Such approximations have the forms of discrete mixtures of small number of standard parametric forms, and so are particularly useful, due to their computational simplicity, in applications where they are to be used as inputs to further analyses, such as simulation.
Keywords:Bayesian density estimation, Discrete mixture distributions, kernel density estimation, mixtures of dirichlet processes