I’ve been working on a project similar to this paper (https://arxiv.org/pdf/1905.09299.pdf) basically you fit a Gaussian process using posterior samples and can then generate more samples by running mcmc taking the gaussian process to be the likelihood ( + prior) . This is advantageous for example if your likelihood is slow to evaluate (and lots of other reasons)
My question is, if I’ve managed to fit a GP (using GPytorch ) how can I pass this to the model used by pyro or numpyro in mcmc. This would be easy to do in something like emcee but I can’t quite see what the parallel would be in pryo .
I think the main problem is don’t fully understand how the sample handler would work in a situation where I have an arbitrary likelihood function rather than a standard distribution ? I also don’t understand how this would work as there is no observed data i.e. I’m not fitting anything to data I just want to draw samples according to the fitted GP posterior surface