Nonparametric Bayesian Density Modeling with Gaussian Processes

Adams, R. P., Murray, I., & MacKay, D. J. C. (2009). Nonparametric Bayesian Density Modeling with Gaussian Processes.
We present the Gaussian process density sampler (GPDS), an exchangeable generative model for use in nonparametric Bayesian density estimation. Samples drawn from the GPDS are consistent with exact, independent samples from a distribution defined by a density that is a transformation of a function drawn from a Gaussian process prior. Our formulation allows us to infer an unknown density from data using Markov chain Monte Carlo, which gives samples from the posterior distribution over density functions and from the predictive distribution on data space. We describe two such MCMC methods. Both methods also allow inference of the hyperparameters of the Gaussian process.
  year = {2009},
  author = {Adams, Ryan P. and Murray, Iain and MacKay, David J.C.},
  title = {Nonparametric {B}ayesian Density Modeling with {G}aussian Processes},
  note = {arXiv:0912.4896 [stat.CO]},
  keywords = {Gaussian processes, Bayesian nonparametrics, density estimation, Bayesian methods, Markov chain Monte Carlo}