I am new to probabilistic programming an I would like to use Turing to perform statistical inference for a relatively complex physical problem, involving a specific model and a set of observations. The model has a few nuisance parameters: that is, the likelihood can be written as P(D \mid \theta, \eta), where D are the data (observations), \theta are the “interesting” parameters and \eta the “nuisance” parameters.
When performing the Bayesian inference I can obtain the posterior P(\theta, \eta \mid D), but given that I am not interested in the nuisance parameters \eta I would anyway marginalize the posterior over them. This is certainly possible, and I believe I know how I could do it with Turing.
Now, the specific form of the likelihood and the assumed prior for \eta let me simplify the problem: I can actually write directly a marginalized likelihood P(D \mid \theta), where I have de-fact removed the nuisance parameters.
The problem is now that I know how to compute P(D \mid \theta), but I do not know anymore how to formulate the problem in Turing: after the marginalization, this function cannot be written anymore in a simple way (for example, it is not anymore the product of the individual likelihoods of each datum). I tried some unsuccessful experiments using directly Turing.@addlogprob!, but I understand this is an advanced topic and there are a number of issues to take into account (including the sampler), so probably this is not the way to go.