I am looking to implement a student's t process as described inShah et al.. The TP implementation in PyMC lacks a .Marginal method needed to properly implement regression with student t processes. This was discussed in a2018 PyMC forum post but hasn't been implemented to my knowledge.

Following the paper, I would expect a model to look something like this, with the noise term applied to the covariance matrix. I'm not entirely sure what the observational model would look like since I am adding in noise at the covariance matrix.

withpm.Model()astp_model:ell=pm.Gamma("ell",alpha=2,beta=1)eta=pm.HalfNormal("eta",sigma=5)noise=pm.HalfNormal("noise",sigma=1.0)k_theta=eta**2*pm.gp.cov.ExpQuad(input_dim=1,ls=ell)# k = kθ + δk=k_theta+pm.gp.cov.WhiteNoise(sigma=noise)# independent noisenu=1+pm.Gamma("nu",alpha=2,beta=1)tp=pm.gp.TP(scale_func=k,nu=nu)        ...

How challenging would this be to implement or are there any workarounds available? The paper provides clear formulas for both marginal likelihood (equations 4-5) and conditional distributions (equation 6).

Thanks in advance!