Using Gaussian Process model to make inference?

For the marginal likelihood GP, the likelihood is always Gaussian, and is wrapped up in the marginal_likelihood function. I’m not exactly sure what the question is here. Are you looking to generate samples from the GP? If so, you’d want to look at using the conditional method after fitting the model. For example:

with gp_model:
  f_pred = gp.conditional('f_pred', X_New)
  pm.sample_posterior_predictive(trace, extend_inferencedata=True)
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