CODEWITHSUNDEEP
pythonpymc3pymc
Serdar
Serdar

Reputation: 35

How to generate multiple posterior distributions under a single PyMC3 model based on multiple likelihoods and a constant prior?

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 fulfil 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?

Upvotes: 0

Views: 33

Answers (1)

aloctavodia
aloctavodia

Reputation: 2070

You can do

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]
idx = np.repeat([0, 1], [7, 17])

with pm.Model() as single_model:
  p = pm.Beta('p', alpha=1, beta=1, shape=2)
  y = pm.Binomial('y', n=1, p=p[idx], observed=data)
  idata = pm.sample()

or

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]]

with pm.Model() as single_model:
    p = pm.Beta('p', alpha=1, beta=1, shape=2)
    y0 = pm.Binomial('y0', n=1, p=p[0], observed=data[0])
    y1 = pm.Binomial('y1', n=1, p=p[1], observed=data[1])
    idata = pm.sample()

As a general rule don't use for-loops, use vectorized versions. Also, PyMC3 is no longer maintained, use PyMC instead.

Upvotes: 0

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