Nonparametric Bayesian Density Modeling with Gaussian Processes

arXiv:0912.4896 [stat.CO] | Google Scholar | BibTex | EndNote


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 de ned 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.


bayesian nonparametrics, density estimation, doubly intractable, gaussian process