Given a positive, normalized kernel and a finite measure on an Euclidean space, we construct a random density by convoluting the kernel with the Dirichlet random probability indexed by the finite measure. The posterior distribution of the random density given a sample is classified. The Bayes estimator of the density function is given.
"On a Class of Bayesian Nonparametric Estimates: I. Density Estimates." Ann. Statist. 12 (1) 351 - 357, March, 1984. https://doi.org/10.1214/aos/1176346412