Bernoulli observations of variable length with a shape parameter

Questions
1

I am attempting to estimate the conversion rate over a number of groups (in the 1000s).

My data is stored as an array of arrays, where each inner array is of variable length, as each group has a different number of observations.

In this issue, the observations were all of the same length and could therefore be stacked. In this issue, a new variable was created for each observation.

My current solution has been to do this:

traces = []

for i in range(len(obs_data)):
    with pm.Model() as model:
        p = pm.Uniform('p', 0, 1)
        obs = pm.Bernoulli('obs', p, observed=obs_data[i])

        trace = pm.sample()
    
    traces.append(trace['p'])

which does work but is inefficient. Am I using the wrong tool for this job?

2

At the very least, you should compile the model once and use pm.Data or theano.shared to update the observed so you dont need to compile the model again.
On a higher level, you use Binomial instead of Bernoulli, which your model translated to:

n = np.asarray([len(k) for k in obs_data])
k = np.asarray([sum(k) for k in obs_data])
with pm.Model() as model:
    p = pm.Uniform('p', 0, 1, shape=len(obs_data))
    obs = pm.Binomial('obs', n, p, observed=k)

    trace = pm.sample()