Yes, exactly! Although the method may seem weird, it is the beginning of my journey down Bayesian analytics so I must use preexisting published methods. Surrogate modeling is employed to generate the large data necessary to use non-informative Uniform priors, since appropriate priors are unknown at this point in my research. I look to use more informative priors in the future when surrogate modeling or large data is not accessible.
Currently, I am importing the data generated from the surrogate model as mu and cov is the covariance function of the outputs from the surrogate model. I turn var* into a single variable theta using theano.tensor.as_tensor_variable(). In the derived likelihood function, it is known that mu is a function of theta, but mu is the posterior prediction dataset from the GP. Is there a way that I can infer the dependence of theta on the existing dataset, mu? If not, do you have any initial ideas to infer theta into the likelihood function in a meaningful way?