Let’s say I have a dataset consisting of two subsets with binary observations. Subsets have the same proportions but different lengths. Based on a fixed Beta prior and those two binomial likelihood distributions, I want to generate two posterior distributions of p. Then, I will collect the mean p’s in an estimation set. Instead of building two different models, I want to fulfill all inferences under a single model. Below you see the PyMC3 model:

with pm.Model() as single_model:
data = [[1, 0, 1, 1, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1]]
estimations = []
p = pm.Beta(‘p’, alpha=1, beta=1)
for i in data:
y = pm.Binomial(‘y’, n=1, p=p, observed=i)
trace = pm.sample(500)
estimations.append(trace[‘p’].mean())

When I run the code, it raises an error like this: ValueError: Variable name y already exists.

I tried to define a shape parameter within the likelihood like ‘shape=len(data)’, but it did not work. How can I generate multiple estimations within the same model?