Is it possible for the observed data be defined as distribution?

1

I have the mean and the standard deviation of my observed data; they are not samples. I would like to know if it is possible to define the observed variable in the pm.MvNormal() as a distribution, because usually I would draw samples from the distribution I know and then feed the model. I thought something like this, but it did not work.

theta = pm.Normal.dist(mu = theta_vt[0], sigma = dist_vt[0])
phi = pm.Normal.dist(mu = phi_vt[0], sigma = dist_vt[1])
p_hat = np.stack((theta, phi))

with pm.Model() as pos_model:
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.
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joint_obs = pm.MvNormal(‘joint’, mu=mu, cov=cov, observed=p_hat)

2

If you want to condition on the mean and std of some data generating process, you would define a PyMC model on the mean/std and observe those.

You can have auxiliary pm.Determinsitic variables that predict new draws from the modeled mean and sigma (not just new means and sigmas) that are not part of the conditioning graph.