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I am trying to compute a Kernel Density from high dimensional data ($n > 2$). The underlying (generative) model is assumed unknown.

The goal is to draw samples from this estimate, in a sense creating synthetic data akin to the underlying distribution.

I was hoping to use Bayesian nonparametrics for this, since the complexity of the model can then grow with the amount of observed data.

The intuition was to use the Dirichlet Process with a Gaussian kernel. DPpackage supports this functionality, but I have little clue on how to interpret the results or sample from them.