I will talk about my current investigations into density estimation with Gaussian process priors. Gaussian processes are useful priors on functions. However, it has been difficult to apply GPs to the density estimation problem, due to the need to know the normalisation constant. Exchange sampling, a recent advance in Markov chain Monte Carlo methods, appears to eliminate the need for this calculation, however, when “fantasy data” can be generated from the prior. To that end, I will show that it is possible to construct a GP-based prior on probability density functions from which data may be exchangeably generated.
