TOWARDS A PRACTICABLE BAYESIAN NONPARAMETRIC DENSITY ESTIMATOR

Nonparametric density estimators smooth the empirical distribution function and are sensitive to the choice of smoothing parameters. This paper develops an hierarchical Bayes formulation for the smoothing problem. The prior distribution for the density function is the logistic normal process, which is a logistic transform of a Gaussian process. The covariance of the Gaussian process is a smoothing kernel and has parameters that control the degree of smoothness. The likelihood function for the smoothing parameters and their posterior density are computed from an approximation of the joint moments of the logistic normal process. The marginal predictive density mixes the conditional predictive density given the smoothing parameters with their posterior distribution. This hierarchial Bayes analysis provides a fully automated, data-dependent method for smoothing and selects the amount of smoothing that is coherent with its prior specification.