  We present a two-stage Metropolis-Hastings algorithm for sampling
probabilistic models, whose log-likelihood is computationally expensive to
evaluate, by using a surrogate Gaussian Process (GP) model. The key feature of
the approach, and the difference w.r.t. previous works, is the ability to learn
the target distribution from scratch (while sampling), and so without the need
of pre-training the GP. This is fundamental for automatic and inference in
Probabilistic Programming Languages In particular, we present an alternative
first stage acceptance scheme by marginalising out the GP distributed function,
which makes the acceptance ratio explicitly dependent on the variance of the
GP. This approach is extended to Metropolis-Adjusted Langevin algorithm (MALA).
