2N+2 parameter inference: sampling all parameters as one?

Questions v5
4

Well in order to understand why all the components of c and d seem to same posterior distribution, I would run the model and try to understand what is going on. c and d seems to be initialized correctly as far as I can see. Maybe the functions are symmetric with respect to different components of c which could result in this?

Some things I can suggest:

  • Try to add stuff to these function that creates more asymmetry between components of c and d (like maybe just an expression that depends on c[0] etc) and see if that changes anything.

  • Use az.plot_posterior on maybe a subset of c to see really that their posteriors are identical (you seem to be using some custom plotting function which can often be the source of error). You can do it via

az.plot_posterior(trace.posterior[["c"]].sel({"group": [0,1]}))
  • You can also sample pairwise differences between components of c and d to see if on average they are different or not via stuff like:
pm.Deterministic("difc", c[:,None] - c[:,None].transpose())

  • Obviously also do az.plot_pcc (after pm.sample_posterior_predictive) to see if your model is fitting reasonably well.

  • Can you generate simulated data with c and d having different components? So you can check whether or not you recover the true parameters.

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