Modeling bivariate beta distributions

[junpenglao]

@valery_kustov

It seems to me that your model considers a different probability of success for each day in both groups.

Exactly, the problem here is that it is difficult (i am tempted to say impossible) to recover latent correlation from samples only, when correlation is not model as a parameter. Imagine trying to model correlated Gaussian with identity Gaussian as prior - you will not be able to recover the correlation:

with pm.Model() as m: 
   x = pm.Normal('x', 0., 100., shape=2) 
   pm.Normal('y', x, 1., observed=np.random.multivariate_normal(np.zeros(2), np.array([[1., .25],[.25, 2.]]), 1000))
   trace = pm.sample()